17 September 2021 11:53:49.654 PM TEST_APPROX_TEST FORTRAN90 version Test the TEST_APPROX library. TEST01 Demonstrate some of the bookkeeping routines. P00_PROB_NUM returns the number of problems. P00_TITLE returns the problem title. P00_LIMIT returns the problem limits. Number of problems = 10 1 "DeBoor example, Mars position". 2 "DeBoor example, roughly linear data". 3 "The pulse data, 0 0 0 0 0 1 0 0 0 0 0". 4 "The jump data, 0 0 0 0 0 1/2 1 1 1 1 1". 5 "DeBoor's Titanium property data". 6 "The Sawtooth data". 7 "Concavity test data". 8 "Extrapolation test data". 9 "Sunspot data, 1700-1960.". 10 "Y = 2 + 5*X + 10*N(0,1).". TEST02 P00_STORY prints the problem "story". Problem 1 This example is due to deBoor. For this example, X is measured in days, and Y records the observed position of Mars in a heliocentric coordinate system. Problem 2 This example is due to deBoor. The data lies roughly along a straight line. Polynomial interpolation is inappropriate. Instead, a least squares approximation should be sought, of the form: F(X) = A + B * X Problem 3 The data is all zero except for a single value of 1 in the center. This data set is interesting because an interpolation method that is "local" will produce an interpolating curve that is exactly zero over most of the outlying intervals, whereas a nonlocal interpolation method may produce a curve that "wiggles" over the entire interpolation interval. Problem 4 Theoretically, the data is a step, 0 to the left of 5, and 1 to the right. To keep things simple, the data is defined to be 0 up to 5 - RADIUS, 1/2 at 5, 1 at 5 + RADIUS and beyond, with RADIUS set to a "small" value, currently 0.01. Some interpolation methods will violently overreact to this jump. Problem 5 This example is due to deBoor. This data represents a temperature dependent property of titanium. Problem 6 This is a data vector. Problem 7 This is a data vector. Problem 8 This example is due to Pierre Blais. Data is only available over the interval [0, 238], but extrapolation is to be used to extend the approximate function to a maximum argument of 1023. The behavior of the extrapolated curve is of great interest. Problem 9 This example is due to Max Waldmeier. This data represents a measure of sunspot activity over the years 1700 to 1960. The X value is the year, and the Y value is a measure of the sunspot activity, which is usually, but not always, an integer. Problem 10 100 uniformly random X values between -2 and 5 were selected, and the formula Y = 2 + 5 * X + 10 * N(0,1) was evaluated, where N(0,1) represents random normal values with 0 mean and unit variance. TEST03 Polynomial interpolation to a vector of data. Problem 1 DeBoor example, Mars position DATA_NUM = 10 Interpolating polynomial order = 10 * 1250.50 1.39140 1255.50 1.38606 * 1260.50 1.37696 1265.50 1.36420 * 1270.50 1.34783 1275.50 1.32792 * 1280.50 1.30456 1285.50 1.27784 * 1290.50 1.24787 1295.50 1.21476 * 1300.50 1.17862 1305.50 1.13958 * 1310.50 1.09776 1315.50 1.05331 * 1320.50 1.00636 1325.50 0.957057 * 1330.50 0.905530 1335.50 0.851920 * 1340.50 0.796420 Problem 2 DeBoor example, roughly linear data DATA_NUM = 11 Interpolating polynomial order = 11 * 1.00000 0.00000 1.50000 -4.83067 * 2.00000 0.600000 2.50000 2.39480 * 3.00000 1.77000 3.50000 1.37568 * 4.00000 1.92000 4.50000 2.78486 * 5.00000 3.31000 5.50000 3.42747 * 6.00000 3.52000 6.50000 3.92580 * 7.00000 4.59000 7.50000 5.14001 * 8.00000 5.31000 8.50000 5.32911 * 9.00000 5.79000 9.50000 6.80032 * 10.0000 7.06000 10.5000 5.07361 * 11.0000 7.17000 Problem 3 The pulse data, 0 0 0 0 0 1 0 0 0 0 0 DATA_NUM = 11 Interpolating polynomial order = 11 * 0.00000 0.00000 0.500000 4.93352 * 1.00000 0.00000 1.50000 -1.00154 * 2.00000 0.00000 2.50000 0.412399 * 3.00000 0.00000 3.50000 -0.320755 * 4.00000 0.00000 4.50000 0.666183 * 5.00000 1.00000 5.50000 0.666183 * 6.00000 0.00000 6.50000 -0.320755 * 7.00000 0.00000 7.50000 0.412399 * 8.00000 0.116573E-13 8.50000 -1.00154 * 9.00000 0.262290E-13 9.50000 4.93352 * 10.0000 0.209832E-12 Problem 4 The jump data, 0 0 0 0 0 1/2 1 1 1 1 1 DATA_NUM = 13 Skipped problem 4 Too big. Problem 5 DeBoor's Titanium property data DATA_NUM = 49 Skipped problem 5 Too big. Problem 6 The Sawtooth data DATA_NUM = 31 Skipped problem 6 Too big. Problem 7 Concavity test data DATA_NUM = 9 Interpolating polynomial order = 9 * 0.00000 0.00000 0.500000E-01 1.32484 * 0.100000 0.900000 0.150000 0.752561 * 0.200000 0.950000 0.250000 1.07856 * 0.300000 0.900000 0.350000 0.489281 * 0.400000 0.100000 0.450000 -0.517323E-01 * 0.500000 0.500000E-01 0.550000 0.190582 * 0.600000 0.500000E-01 0.700000 -1.36104 * 0.800000 0.200000 0.900000 11.7975 * 1.00000 1.00000 Problem 8 Extrapolation test data DATA_NUM = 12 Interpolating polynomial order = 12 * 0.00000 0.00000 35.5000 53263.6 * 71.0000 7.75540 87.5000 -365.169 * 104.000 19.7062 119.500 52.6291 * 135.000 35.5379 140.000 38.2108 * 145.000 42.9154 152.500 50.0208 * 160.000 54.7752 170.500 59.3723 * 181.000 66.7587 187.000 72.5336 * 193.000 78.4929 199.000 84.1117 * 205.000 89.7683 210.000 95.2479 * 215.000 101.746 220.000 108.479 * 225.000 113.482 231.500 116.128 * 238.000 135.457 Problem 9 Sunspot data, 1700-1960. DATA_NUM = 261 Skipped problem 9 Too big. Problem 10 Y = 2 + 5*X + 10*N(0,1). DATA_NUM = 100 Skipped problem 10 Too big. TEST04 Linear spline interpolation. Problem 1 DeBoor example, Mars position X Y Y' * 1250.50 1.39140 -0.144400E-02 1255.50 1.38418 -0.144400E-02 * 1260.50 1.37696 -0.291300E-02 1265.50 1.36240 -0.291300E-02 * 1270.50 1.34783 -0.432700E-02 1275.50 1.32620 -0.432700E-02 * 1280.50 1.30456 -0.566900E-02 1285.50 1.27622 -0.566900E-02 * 1290.50 1.24787 -0.692500E-02 1295.50 1.21325 -0.692500E-02 * 1300.50 1.17862 -0.808600E-02 1305.50 1.13819 -0.808600E-02 * 1310.50 1.09776 -0.914000E-02 1315.50 1.05206 -0.914000E-02 * 1320.50 1.00636 -0.100830E-01 1325.50 0.955945 -0.100830E-01 * 1330.50 0.905530 -0.109110E-01 1335.50 0.850975 -0.109110E-01 * 1340.50 0.796420 -0.109110E-01 Problem 2 DeBoor example, roughly linear data X Y Y' * 1.00000 0.00000 0.600000 1.50000 0.300000 0.600000 * 2.00000 0.600000 1.17000 2.50000 1.18500 1.17000 * 3.00000 1.77000 0.150000 3.50000 1.84500 0.150000 * 4.00000 1.92000 1.39000 4.50000 2.61500 1.39000 * 5.00000 3.31000 0.210000 5.50000 3.41500 0.210000 * 6.00000 3.52000 1.07000 6.50000 4.05500 1.07000 * 7.00000 4.59000 0.720000 7.50000 4.95000 0.720000 * 8.00000 5.31000 0.480000 8.50000 5.55000 0.480000 * 9.00000 5.79000 1.27000 9.50000 6.42500 1.27000 * 10.0000 7.06000 0.110000 10.5000 7.11500 0.110000 * 11.0000 7.17000 0.110000 Problem 3 The pulse data, 0 0 0 0 0 1 0 0 0 0 0 X Y Y' * 0.00000 0.00000 0.00000 0.500000 0.00000 0.00000 * 1.00000 0.00000 0.00000 1.50000 0.00000 0.00000 * 2.00000 0.00000 0.00000 2.50000 0.00000 0.00000 * 3.00000 0.00000 0.00000 3.50000 0.00000 0.00000 * 4.00000 0.00000 1.00000 4.50000 0.500000 1.00000 * 5.00000 1.00000 -1.00000 5.50000 0.500000 -1.00000 * 6.00000 0.00000 0.00000 6.50000 0.00000 0.00000 * 7.00000 0.00000 0.00000 7.50000 0.00000 0.00000 * 8.00000 0.00000 0.00000 8.50000 0.00000 0.00000 * 9.00000 0.00000 0.00000 9.50000 0.00000 0.00000 * 10.0000 0.00000 0.00000 Problem 4 The jump data, 0 0 0 0 0 1/2 1 1 1 1 1 X Y Y' * 0.00000 0.00000 0.00000 0.416667 0.00000 0.00000 * 0.833333 0.00000 0.00000 1.25000 0.00000 0.00000 * 1.66667 0.00000 0.00000 2.08333 0.00000 0.00000 * 2.50000 0.00000 0.00000 2.91667 0.00000 0.00000 * 3.33333 0.00000 0.00000 3.75000 0.00000 0.00000 * 4.16667 0.00000 0.00000 4.58333 0.00000 0.00000 * 5.00000 0.500000 50.0000 5.41667 1.00000 0.00000 * 5.83333 1.00000 0.00000 6.25000 1.00000 0.00000 * 6.66667 1.00000 0.00000 7.08333 1.00000 0.00000 * 7.50000 1.00000 0.00000 7.91667 1.00000 0.00000 * 8.33333 1.00000 0.00000 8.75000 1.00000 0.00000 * 9.16667 1.00000 0.00000 9.58333 1.00000 0.00000 * 10.0000 1.00000 0.00000 Problem 5 DeBoor's Titanium property data X Y Y' * 595.000 0.644000 -0.220000E-02 600.000 0.633000 -0.220000E-02 * 605.000 0.622000 0.160000E-02 610.000 0.630000 0.160000E-02 * 615.000 0.638000 0.110000E-02 620.000 0.643500 0.110000E-02 * 625.000 0.649000 0.300000E-03 630.000 0.650500 0.300000E-03 * 635.000 0.652000 -0.130000E-02 640.000 0.645500 -0.130000E-02 * 645.000 0.639000 0.700000E-03 650.000 0.642500 0.700000E-03 * 655.000 0.646000 0.110000E-02 660.000 0.651500 0.110000E-02 * 665.000 0.657000 -0.500000E-03 670.000 0.654500 -0.500000E-03 * 675.000 0.652000 0.300000E-03 680.000 0.653500 0.300000E-03 * 685.000 0.655000 -0.110000E-02 690.000 0.649500 -0.110000E-02 * 695.000 0.644000 0.190000E-02 700.000 0.653500 0.190000E-02 * 705.000 0.663000 0.00000 710.000 0.663000 0.00000 * 715.000 0.663000 0.500000E-03 720.000 0.665500 0.500000E-03 * 725.000 0.668000 0.800000E-03 730.000 0.672000 0.800000E-03 * 735.000 0.676000 0.00000 740.000 0.676000 0.00000 * 745.000 0.676000 0.100000E-02 750.000 0.681000 0.100000E-02 * 755.000 0.686000 -0.700000E-03 760.000 0.682500 -0.700000E-03 * 765.000 0.679000 -0.100000E-03 770.000 0.678500 -0.100000E-03 * 775.000 0.678000 0.500000E-03 780.000 0.680500 0.500000E-03 * 785.000 0.683000 0.110000E-02 790.000 0.688500 0.110000E-02 * 795.000 0.694000 0.500000E-03 800.000 0.696500 0.500000E-03 * 805.000 0.699000 0.110000E-02 810.000 0.704500 0.110000E-02 * 815.000 0.710000 0.200000E-02 820.000 0.720000 0.200000E-02 * 825.000 0.730000 0.330000E-02 830.000 0.746500 0.330000E-02 * 835.000 0.763000 0.490000E-02 840.000 0.787500 0.490000E-02 * 845.000 0.812000 0.950000E-02 850.000 0.859500 0.950000E-02 * 855.000 0.907000 0.137000E-01 860.000 0.975500 0.137000E-01 * 865.000 1.04400 0.292000E-01 870.000 1.19000 0.292000E-01 * 875.000 1.33600 0.545000E-01 880.000 1.60850 0.545000E-01 * 885.000 1.88100 0.288000E-01 890.000 2.02500 0.288000E-01 * 895.000 2.16900 -0.940000E-02 900.000 2.12200 -0.940000E-02 * 905.000 2.07500 -0.477000E-01 910.000 1.83650 -0.477000E-01 * 915.000 1.59800 -0.387000E-01 920.000 1.40450 -0.387000E-01 * 925.000 1.21100 -0.295000E-01 930.000 1.06350 -0.295000E-01 * 935.000 0.916000 -0.170000E-01 940.000 0.831000 -0.170000E-01 * 945.000 0.746000 -0.740000E-02 950.000 0.709000 -0.740000E-02 * 955.000 0.672000 -0.450000E-02 960.000 0.649500 -0.450000E-02 * 965.000 0.627000 -0.120000E-02 970.000 0.621000 -0.120000E-02 * 975.000 0.615000 -0.800000E-03 980.000 0.611000 -0.800000E-03 * 985.000 0.607000 -0.100000E-03 990.000 0.606500 -0.100000E-03 * 995.000 0.606000 0.300000E-03 1000.00 0.607500 0.300000E-03 * 1005.00 0.609000 -0.600000E-03 1010.00 0.606000 -0.600000E-03 * 1015.00 0.603000 -0.200000E-03 1020.00 0.602000 -0.200000E-03 * 1025.00 0.601000 0.200000E-03 1030.00 0.602000 0.200000E-03 * 1035.00 0.603000 -0.200000E-03 1040.00 0.602000 -0.200000E-03 * 1045.00 0.601000 0.100000E-02 1050.00 0.606000 0.100000E-02 * 1055.00 0.611000 -0.100000E-02 1060.00 0.606000 -0.100000E-02 * 1065.00 0.601000 0.700000E-03 1070.00 0.604500 0.700000E-03 * 1075.00 0.608000 0.700000E-03 Problem 6 The Sawtooth data X Y Y' * 0.00000 0.00000 2.00000 0.833333E-01 0.166667 2.00000 * 0.166667 0.333333 2.00000 0.250000 0.500000 2.00000 * 0.333333 0.666667 2.00000 0.416667 0.833333 2.00000 * 0.500000 1.00000 -2.00000 0.583333 0.833333 -2.00000 * 0.666667 0.666667 -2.00000 0.750000 0.500000 -2.00000 * 0.833333 0.333333 -2.00000 0.916667 0.166667 -2.00000 * 1.00000 0.00000 2.00000 1.08333 0.166667 2.00000 * 1.16667 0.333333 2.00000 1.25000 0.500000 2.00000 * 1.33333 0.666667 2.00000 1.41667 0.833333 2.00000 * 1.50000 1.00000 -2.00000 1.58333 0.833333 -2.00000 * 1.66667 0.666667 -2.00000 1.75000 0.500000 -2.00000 * 1.83333 0.333333 -2.00000 1.91667 0.166667 -2.00000 * 2.00000 0.00000 2.00000 2.08333 0.166667 2.00000 * 2.16667 0.333333 2.00000 2.25000 0.500000 2.00000 * 2.33333 0.666667 2.00000 2.41667 0.833333 2.00000 * 2.50000 1.00000 -2.00000 2.58333 0.833333 -2.00000 * 2.66667 0.666667 -2.00000 2.75000 0.500000 -2.00000 * 2.83333 0.333333 -2.00000 2.91667 0.166667 -2.00000 * 3.00000 0.00000 2.00000 3.08333 0.166667 2.00000 * 3.16667 0.333333 2.00000 3.25000 0.500000 2.00000 * 3.33333 0.666667 2.00000 3.41667 0.833333 2.00000 * 3.50000 1.00000 -2.00000 3.58333 0.833333 -2.00000 * 3.66667 0.666667 -2.00000 3.75000 0.500000 -2.00000 * 3.83333 0.333333 -2.00000 3.91667 0.166667 -2.00000 * 4.00000 0.00000 2.00000 4.08333 0.166667 2.00000 * 4.16667 0.333333 2.00000 4.25000 0.500000 2.00000 * 4.33333 0.666667 2.00000 4.41667 0.833333 2.00000 * 4.50000 1.00000 -2.00000 4.58333 0.833333 -2.00000 * 4.66667 0.666667 -2.00000 4.75000 0.500000 -2.00000 * 4.83333 0.333333 -2.00000 4.91667 0.166667 -2.00000 * 5.00000 0.00000 -2.00000 Problem 7 Concavity test data X Y Y' * 0.00000 0.00000 9.00000 0.625000E-01 0.562500 9.00000 * 0.125000 0.912500 0.500000 0.187500 0.943750 0.500000 * 0.250000 0.925000 -0.500000 0.312500 0.800000 -8.00000 * 0.375000 0.300000 -8.00000 0.437500 0.812500E-01 -0.500000 * 0.500000 0.500000E-01 0.00000 0.562500 0.500000E-01 0.00000 * 0.625000 0.687500E-01 0.750000 0.687500 0.115625 0.750000 * 0.750000 0.162500 0.750000 0.812500 0.250000 4.00000 * 0.875000 0.500000 4.00000 0.937500 0.750000 4.00000 * 1.00000 1.00000 4.00000 Problem 8 Extrapolation test data X Y Y' * 0.00000 0.00000 0.109231 10.8182 1.18168 0.109231 * 21.6364 2.36336 0.109231 32.4545 3.54504 0.109231 * 43.2727 4.72672 0.109231 54.0909 5.90840 0.109231 * 64.9091 7.09008 0.109231 75.7273 9.46736 0.362145 * 86.5455 13.3851 0.362145 97.3636 17.3029 0.362145 * 108.182 21.8418 0.510699 119.000 27.3667 0.510699 * 129.818 32.8915 0.510699 140.636 39.6961 0.737751 * 151.455 48.0187 0.790655 162.273 56.0721 0.570640 * 173.091 62.2454 0.570640 183.909 69.6033 0.977851 * 194.727 80.1158 0.939623 205.545 90.4217 1.19777 * 216.364 103.346 1.17364 227.182 117.170 1.69032 * 238.000 135.457 1.69032 Problem 9 Sunspot data, 1700-1960. X Y Y' * 1700.00 5.00000 6.00000 1700.50 8.00000 6.00000 * 1701.00 11.0000 5.00000 1701.50 13.5000 5.00000 * 1702.00 16.0000 7.00000 1702.50 19.5000 7.00000 * 1703.00 23.0000 13.0000 1703.50 29.5000 13.0000 * 1704.00 36.0000 22.0000 1704.50 47.0000 22.0000 * 1705.00 58.0000 -29.0000 1705.50 43.5000 -29.0000 * 1706.00 29.0000 -9.00000 1706.50 24.5000 -9.00000 * 1707.00 20.0000 -10.0000 1707.50 15.0000 -10.0000 * 1708.00 10.0000 -2.00000 1708.50 9.00000 -2.00000 * 1709.00 8.00000 -5.00000 1709.50 5.50000 -5.00000 * 1710.00 3.00000 -3.00000 1710.50 1.50000 -3.00000 * 1711.00 0.00000 0.00000 1711.50 0.00000 0.00000 * 1712.00 0.00000 2.00000 1712.50 1.00000 2.00000 * 1713.00 2.00000 9.00000 1713.50 6.50000 9.00000 * 1714.00 11.0000 16.0000 1714.50 19.0000 16.0000 * 1715.00 27.0000 20.0000 1715.50 37.0000 20.0000 * 1716.00 47.0000 16.0000 1716.50 55.0000 16.0000 * 1717.00 63.0000 -3.00000 1717.50 61.5000 -3.00000 * 1718.00 60.0000 -21.0000 1718.50 49.5000 -21.0000 * 1719.00 39.0000 -11.0000 1719.50 33.5000 -11.0000 * 1720.00 28.0000 -2.00000 1720.50 27.0000 -2.00000 * 1721.00 26.0000 -4.00000 1721.50 24.0000 -4.00000 * 1722.00 22.0000 -11.0000 1722.50 16.5000 -11.0000 * 1723.00 11.0000 10.0000 1723.50 16.0000 10.0000 * 1724.00 21.0000 19.0000 1724.50 30.5000 19.0000 * 1725.00 40.0000 38.0000 1725.50 59.0000 38.0000 * 1726.00 78.0000 44.0000 1726.50 100.000 44.0000 * 1727.00 122.000 -19.0000 1727.50 112.500 -19.0000 * 1728.00 103.000 -30.0000 1728.50 88.0000 -30.0000 * 1729.00 73.0000 -26.0000 1729.50 60.0000 -26.0000 * 1730.00 47.0000 -12.0000 1730.50 41.0000 -12.0000 * 1731.00 35.0000 -24.0000 1731.50 23.0000 -24.0000 * 1732.00 11.0000 -6.00000 1732.50 8.00000 -6.00000 * 1733.00 5.00000 11.0000 1733.50 10.5000 11.0000 * 1734.00 16.0000 18.0000 1734.50 25.0000 18.0000 * 1735.00 34.0000 36.0000 1735.50 52.0000 36.0000 * 1736.00 70.0000 11.0000 1736.50 75.5000 11.0000 * 1737.00 81.0000 30.0000 1737.50 96.0000 30.0000 * 1738.00 111.000 -10.0000 1738.50 106.000 -10.0000 * 1739.00 101.000 -28.0000 1739.50 87.0000 -28.0000 * 1740.00 73.0000 -33.0000 1740.50 56.5000 -33.0000 * 1741.00 40.0000 -20.0000 1741.50 30.0000 -20.0000 * 1742.00 20.0000 -4.00000 1742.50 18.0000 -4.00000 * 1743.00 16.0000 -11.0000 1743.50 10.5000 -11.0000 * 1744.00 5.00000 6.00000 1744.50 8.00000 6.00000 * 1745.00 11.0000 11.0000 1745.50 16.5000 11.0000 * 1746.00 22.0000 18.0000 1746.50 31.0000 18.0000 * 1747.00 40.0000 20.0000 1747.50 50.0000 20.0000 * 1748.00 60.0000 20.9000 1748.50 70.4500 20.9000 * 1749.00 80.9000 2.50000 1749.50 82.1500 2.50000 * 1750.00 83.4000 -35.7000 1750.50 65.5500 -35.7000 * 1751.00 47.7000 0.100000 1751.50 47.7500 0.100000 * 1752.00 47.8000 -17.1000 1752.50 39.2500 -17.1000 * 1753.00 30.7000 -18.5000 1753.50 21.4500 -18.5000 * 1754.00 12.2000 -2.60000 1754.50 10.9000 -2.60000 * 1755.00 9.60000 0.600000 1755.50 9.90000 0.600000 * 1756.00 10.2000 22.2000 1756.50 21.3000 22.2000 * 1757.00 32.4000 15.2000 1757.50 40.0000 15.2000 * 1758.00 47.6000 6.40000 1758.50 50.8000 6.40000 * 1759.00 54.0000 8.90000 1759.50 58.4500 8.90000 * 1760.00 62.9000 23.0000 1760.50 74.4000 23.0000 * 1761.00 85.9000 -24.7000 1761.50 73.5500 -24.7000 * 1762.00 61.2000 -16.1000 1762.50 53.1500 -16.1000 * 1763.00 45.1000 -8.70000 1763.50 40.7500 -8.70000 * 1764.00 36.4000 -15.5000 1764.50 28.6500 -15.5000 * 1765.00 20.9000 -9.50000 1765.50 16.1500 -9.50000 * 1766.00 11.4000 26.4000 1766.50 24.6000 26.4000 * 1767.00 37.8000 32.0000 1767.50 53.8000 32.0000 * 1768.00 69.8000 36.3000 1768.50 87.9500 36.3000 * 1769.00 106.100 -5.30000 1769.50 103.450 -5.30000 * 1770.00 100.800 -19.2000 1770.50 91.2000 -19.2000 * 1771.00 81.6000 -15.1000 1771.50 74.0500 -15.1000 * 1772.00 66.5000 -31.7000 1772.50 50.6500 -31.7000 * 1773.00 34.8000 -4.20000 1773.50 32.7000 -4.20000 * 1774.00 30.6000 -23.6000 1774.50 18.8000 -23.6000 * 1775.00 7.00000 12.8000 1775.50 13.4000 12.8000 * 1776.00 19.8000 72.7000 1776.50 56.1500 72.7000 * 1777.00 92.5000 61.9000 1777.50 123.450 61.9000 * 1778.00 154.400 -28.5000 1778.50 140.150 -28.5000 * 1779.00 125.900 -41.1000 1779.50 105.350 -41.1000 * 1780.00 84.8000 -16.7000 1780.50 76.4500 -16.7000 * 1781.00 68.1000 -29.6000 1781.50 53.3000 -29.6000 * 1782.00 38.5000 -15.7000 1782.50 30.6500 -15.7000 * 1783.00 22.8000 -12.6000 1783.50 16.5000 -12.6000 * 1784.00 10.2000 13.9000 1784.50 17.1500 13.9000 * 1785.00 24.1000 58.8000 1785.50 53.5000 58.8000 * 1786.00 82.9000 49.1000 1786.50 107.450 49.1000 * 1787.00 132.000 -1.10000 1787.50 131.450 -1.10000 * 1788.00 130.900 -12.8000 1788.50 124.500 -12.8000 * 1789.00 118.100 -28.2000 1789.50 104.000 -28.2000 * 1790.00 89.9000 -23.3000 1790.50 78.2500 -23.3000 * 1791.00 66.6000 -6.60000 1791.50 63.3000 -6.60000 * 1792.00 60.0000 -13.1000 1792.50 53.4500 -13.1000 * 1793.00 46.9000 -5.90000 1793.50 43.9500 -5.90000 * 1794.00 41.0000 -19.7000 1794.50 31.1500 -19.7000 * 1795.00 21.3000 -5.30000 1795.50 18.6500 -5.30000 * 1796.00 16.0000 -9.60000 1796.50 11.2000 -9.60000 * 1797.00 6.40000 -2.30000 1797.50 5.25000 -2.30000 * 1798.00 4.10000 2.70000 1798.50 5.45000 2.70000 * 1799.00 6.80000 7.70000 1799.50 10.6500 7.70000 * 1800.00 14.5000 19.5000 1800.50 24.2500 19.5000 * 1801.00 34.0000 11.0000 1801.50 39.5000 11.0000 * 1802.00 45.0000 -1.90000 1802.50 44.0500 -1.90000 * 1803.00 43.1000 4.40000 1803.50 45.3000 4.40000 * 1804.00 47.5000 -5.30000 1804.50 44.8500 -5.30000 * 1805.00 42.2000 -14.1000 1805.50 35.1500 -14.1000 * 1806.00 28.1000 -18.0000 1806.50 19.1000 -18.0000 * 1807.00 10.1000 -2.00000 1807.50 9.10000 -2.00000 * 1808.00 8.10000 -5.60000 1808.50 5.30000 -5.60000 * 1809.00 2.50000 -2.50000 1809.50 1.25000 -2.50000 * 1810.00 0.00000 1.40000 1810.50 0.700000 1.40000 * 1811.00 1.40000 3.60000 1811.50 3.20000 3.60000 * 1812.00 5.00000 7.20000 1812.50 8.60000 7.20000 * 1813.00 12.2000 1.70000 1813.50 13.0500 1.70000 * 1814.00 13.9000 21.5000 1814.50 24.6500 21.5000 * 1815.00 35.4000 10.4000 1815.50 40.6000 10.4000 * 1816.00 45.8000 -4.70000 1816.50 43.4500 -4.70000 * 1817.00 41.1000 -11.0000 1817.50 35.6000 -11.0000 * 1818.00 30.1000 -6.20000 1818.50 27.0000 -6.20000 * 1819.00 23.9000 -8.30000 1819.50 19.7500 -8.30000 * 1820.00 15.6000 -9.00000 1820.50 11.1000 -9.00000 * 1821.00 6.60000 -2.60000 1821.50 5.30000 -2.60000 * 1822.00 4.00000 -2.20000 1822.50 2.90000 -2.20000 * 1823.00 1.80000 6.70000 1823.50 5.15000 6.70000 * 1824.00 8.50000 8.10000 1824.50 12.5500 8.10000 * 1825.00 16.6000 19.7000 1825.50 26.4500 19.7000 * 1826.00 36.3000 13.3000 1826.50 42.9500 13.3000 * 1827.00 49.6000 14.6000 1827.50 56.9000 14.6000 * 1828.00 64.2000 2.80000 1828.50 65.6000 2.80000 * 1829.00 67.0000 3.90000 1829.50 68.9500 3.90000 * 1830.00 70.9000 -23.1000 1830.50 59.3500 -23.1000 * 1831.00 47.8000 -20.3000 1831.50 37.6500 -20.3000 * 1832.00 27.5000 -19.0000 1832.50 18.0000 -19.0000 * 1833.00 8.50000 4.70000 1833.50 10.8500 4.70000 * 1834.00 13.2000 43.7000 1834.50 35.0500 43.7000 * 1835.00 56.9000 64.6000 1835.50 89.2000 64.6000 * 1836.00 121.500 16.8000 1836.50 129.900 16.8000 * 1837.00 138.300 -35.1000 1837.50 120.750 -35.1000 * 1838.00 103.200 -17.5000 1838.50 94.4500 -17.5000 * 1839.00 85.7000 -21.1000 1839.50 75.1500 -21.1000 * 1840.00 64.6000 -27.9000 1840.50 50.6500 -27.9000 * 1841.00 36.7000 -12.5000 1841.50 30.4500 -12.5000 * 1842.00 24.2000 -13.5000 1842.50 17.4500 -13.5000 * 1843.00 10.7000 4.30000 1843.50 12.8500 4.30000 * 1844.00 15.0000 25.1000 1844.50 27.5500 25.1000 * 1845.00 40.1000 21.4000 1845.50 50.8000 21.4000 * 1846.00 61.5000 37.0000 1846.50 80.0000 37.0000 * 1847.00 98.5000 26.2000 1847.50 111.600 26.2000 * 1848.00 124.700 -28.4000 1848.50 110.500 -28.4000 * 1849.00 96.3000 -29.7000 1849.50 81.4500 -29.7000 * 1850.00 66.6000 -2.10000 1850.50 65.5500 -2.10000 * 1851.00 64.5000 -10.4000 1851.50 59.3000 -10.4000 * 1852.00 54.1000 -15.1000 1852.50 46.5500 -15.1000 * 1853.00 39.0000 -18.4000 1853.50 29.8000 -18.4000 * 1854.00 20.6000 -13.9000 1854.50 13.6500 -13.9000 * 1855.00 6.70000 -2.40000 1855.50 5.50000 -2.40000 * 1856.00 4.30000 18.4000 1856.50 13.5000 18.4000 * 1857.00 22.7000 32.1000 1857.50 38.7500 32.1000 * 1858.00 54.8000 39.0000 1858.50 74.3000 39.0000 * 1859.00 93.8000 2.00000 1859.50 94.8000 2.00000 * 1860.00 95.8000 -18.6000 1860.50 86.5000 -18.6000 * 1861.00 77.2000 -18.1000 1861.50 68.1500 -18.1000 * 1862.00 59.1000 -15.1000 1862.50 51.5500 -15.1000 * 1863.00 44.0000 3.00000 1863.50 45.5000 3.00000 * 1864.00 47.0000 -16.5000 1864.50 38.7500 -16.5000 * 1865.00 30.5000 -14.2000 1865.50 23.4000 -14.2000 * 1866.00 16.3000 -9.00000 1866.50 11.8000 -9.00000 * 1867.00 7.30000 30.3000 1867.50 22.4500 30.3000 * 1868.00 37.6000 36.4000 1868.50 55.8000 36.4000 * 1869.00 74.0000 65.0000 1869.50 106.500 65.0000 * 1870.00 139.000 -27.8000 1870.50 125.100 -27.8000 * 1871.00 111.200 -9.60000 1871.50 106.400 -9.60000 * 1872.00 101.600 -35.4000 1872.50 83.9000 -35.4000 * 1873.00 66.2000 -21.5000 1873.50 55.4500 -21.5000 * 1874.00 44.7000 -27.7000 1874.50 30.8500 -27.7000 * 1875.00 17.0000 -5.70000 1875.50 14.1500 -5.70000 * 1876.00 11.3000 1.10000 1876.50 11.8500 1.10000 * 1877.00 12.4000 -9.00000 1877.50 7.90000 -9.00000 * 1878.00 3.40000 2.60000 1878.50 4.70000 2.60000 * 1879.00 6.00000 26.3000 1879.50 19.1500 26.3000 * 1880.00 32.3000 22.0000 1880.50 43.3000 22.0000 * 1881.00 54.3000 5.40000 1881.50 57.0000 5.40000 * 1882.00 59.7000 4.00000 1882.50 61.7000 4.00000 * 1883.00 63.7000 -0.200000 1883.50 63.6000 -0.200000 * 1884.00 63.5000 -11.3000 1884.50 57.8500 -11.3000 * 1885.00 52.2000 -26.8000 1885.50 38.8000 -26.8000 * 1886.00 25.4000 -12.3000 1886.50 19.2500 -12.3000 * 1887.00 13.1000 -6.30000 1887.50 9.95000 -6.30000 * 1888.00 6.80000 -0.500000 1888.50 6.55000 -0.500000 * 1889.00 6.30000 0.800000 1889.50 6.70000 0.800000 * 1890.00 7.10000 28.5000 1890.50 21.3500 28.5000 * 1891.00 35.6000 37.4000 1891.50 54.3000 37.4000 * 1892.00 73.0000 12.1000 1892.50 79.0500 12.1000 * 1893.00 85.1000 -7.10000 1893.50 81.5500 -7.10000 * 1894.00 78.0000 -14.0000 1894.50 71.0000 -14.0000 * 1895.00 64.0000 -22.2000 1895.50 52.9000 -22.2000 * 1896.00 41.8000 -15.6000 1896.50 34.0000 -15.6000 * 1897.00 26.2000 0.500000 1897.50 26.4500 0.500000 * 1898.00 26.7000 -14.6000 1898.50 19.4000 -14.6000 * 1899.00 12.1000 -2.60000 1899.50 10.8000 -2.60000 * 1900.00 9.50000 -6.80000 1900.50 6.10000 -6.80000 * 1901.00 2.70000 2.30000 1901.50 3.85000 2.30000 * 1902.00 5.00000 19.4000 1902.50 14.7000 19.4000 * 1903.00 24.4000 17.6000 1903.50 33.2000 17.6000 * 1904.00 42.0000 21.5000 1904.50 52.7500 21.5000 * 1905.00 63.5000 -9.70000 1905.50 58.6500 -9.70000 * 1906.00 53.8000 8.20000 1906.50 57.9000 8.20000 * 1907.00 62.0000 -13.5000 1907.50 55.2500 -13.5000 * 1908.00 48.5000 -4.60000 1908.50 46.2000 -4.60000 * 1909.00 43.9000 -25.3000 1909.50 31.2500 -25.3000 * 1910.00 18.6000 -12.9000 1910.50 12.1500 -12.9000 * 1911.00 5.70000 -2.10000 1911.50 4.65000 -2.10000 * 1912.00 3.60000 -2.20000 1912.50 2.50000 -2.20000 * 1913.00 1.40000 8.20000 1913.50 5.50000 8.20000 * 1914.00 9.60000 37.8000 1914.50 28.5000 37.8000 * 1915.00 47.4000 9.70000 1915.50 52.2500 9.70000 * 1916.00 57.1000 46.8000 1916.50 80.5000 46.8000 * 1917.00 103.900 -23.3000 1917.50 92.2500 -23.3000 * 1918.00 80.6000 -17.0000 1918.50 72.1000 -17.0000 * 1919.00 63.6000 -26.0000 1919.50 50.6000 -26.0000 * 1920.00 37.6000 -11.5000 1920.50 31.8500 -11.5000 * 1921.00 26.1000 -11.9000 1921.50 20.1500 -11.9000 * 1922.00 14.2000 -8.40000 1922.50 10.0000 -8.40000 * 1923.00 5.80000 10.9000 1923.50 11.2500 10.9000 * 1924.00 16.7000 27.6000 1924.50 30.5000 27.6000 * 1925.00 44.3000 19.6000 1925.50 54.1000 19.6000 * 1926.00 63.9000 5.10000 1926.50 66.4500 5.10000 * 1927.00 69.0000 8.80000 1927.50 73.4000 8.80000 * 1928.00 77.8000 -12.9000 1928.50 71.3500 -12.9000 * 1929.00 64.9000 -29.2000 1929.50 50.3000 -29.2000 * 1930.00 35.7000 -14.5000 1930.50 28.4500 -14.5000 * 1931.00 21.2000 -10.1000 1931.50 16.1500 -10.1000 * 1932.00 11.1000 -5.40000 1932.50 8.40000 -5.40000 * 1933.00 5.70000 3.00000 1933.50 7.20000 3.00000 * 1934.00 8.70000 27.4000 1934.50 22.4000 27.4000 * 1935.00 36.1000 43.6000 1935.50 57.9000 43.6000 * 1936.00 79.7000 34.7000 1936.50 97.0500 34.7000 * 1937.00 114.400 -4.80000 1937.50 112.000 -4.80000 * 1938.00 109.600 -20.8000 1938.50 99.2000 -20.8000 * 1939.00 88.8000 -21.0000 1939.50 78.3000 -21.0000 * 1940.00 67.8000 -20.3000 1940.50 57.6500 -20.3000 * 1941.00 47.5000 -16.9000 1941.50 39.0500 -16.9000 * 1942.00 30.6000 -14.3000 1942.50 23.4500 -14.3000 * 1943.00 16.3000 -6.70000 1943.50 12.9500 -6.70000 * 1944.00 9.60000 23.6000 1944.50 21.4000 23.6000 * 1945.00 33.2000 59.4000 1945.50 62.9000 59.4000 * 1946.00 92.6000 59.0000 1946.50 122.100 59.0000 * 1947.00 151.600 -15.3000 1947.50 143.950 -15.3000 * 1948.00 136.300 -1.60000 1948.50 135.500 -1.60000 * 1949.00 134.700 -50.8000 1949.50 109.300 -50.8000 * 1950.00 83.9000 -14.5000 1950.50 76.6500 -14.5000 * 1951.00 69.4000 -37.9000 1951.50 50.4500 -37.9000 * 1952.00 31.5000 -17.6000 1952.50 22.7000 -17.6000 * 1953.00 13.9000 -9.50000 1953.50 9.15000 -9.50000 * 1954.00 4.40000 33.6000 1954.50 21.2000 33.6000 * 1955.00 38.0000 103.700 1955.50 89.8500 103.700 * 1956.00 141.700 48.5000 1956.50 165.950 48.5000 * 1957.00 190.200 -5.40000 1957.50 187.500 -5.40000 * 1958.00 184.800 -25.8000 1958.50 171.900 -25.8000 * 1959.00 159.000 -46.7000 1959.50 135.650 -46.7000 * 1960.00 112.300 -46.7000 Problem 10 Y = 2 + 5*X + 10*N(0,1). X Y Y' * -1.99350 -1.89180 -64.0190 -1.95873 -4.11792 -64.0190 * -1.92395 -6.34403 -64.0190 -1.88918 -8.57015 -64.0190 * -1.85441 -7.87361 -321.302 -1.81964 -19.0462 -321.302 * -1.78486 -20.9521 35.9813 -1.75009 -19.7009 35.9813 * -1.71532 -18.4497 35.9813 -1.68055 -17.1986 35.9813 * -1.64577 -14.9936 97.0144 -1.61100 -11.6202 97.0144 * -1.57623 -9.53931 40.5019 -1.54145 -8.13095 40.5019 * -1.50668 -6.72259 40.5019 -1.47191 -5.31422 40.5019 * -1.43714 -3.55334 108.773 -1.40236 0.228995 108.773 * -1.36759 4.01133 108.773 -1.33282 5.68747 -77.9158 * -1.29805 2.97812 -77.9158 -1.26327 0.268775 -77.9158 * -1.22850 -2.44057 -77.9158 -1.19373 -5.14992 -77.9158 * -1.15895 7.36437 1005.97 -1.12418 7.44345 -41.5435 * -1.08941 5.99886 -41.5435 -1.05464 4.55428 -41.5435 * -1.01986 3.10970 -41.5435 -0.985091 1.97352 46.3426 * -0.950318 3.58498 46.3426 -0.915545 5.19644 46.3426 * -0.880773 6.80790 46.3426 -0.846000 8.41936 46.3426 * -0.811227 7.62166 -241.395 -0.776455 -1.39152 -1200.74 * -0.741682 -13.7458 -184.124 -0.706909 4.87261 -106.897 * -0.672136 1.15550 -106.897 -0.637364 -2.56161 -106.897 * -0.602591 -6.38680 -112.066 -0.567818 -6.06394 10.3087 * -0.533045 -5.70547 10.3087 -0.498273 -5.34701 10.3087 * -0.463500 -4.98855 10.3087 -0.428727 -4.63009 10.3087 * -0.393955 -4.27163 10.3087 -0.359182 -3.91316 10.3087 * -0.324409 -3.55470 10.3087 -0.289636 -3.19624 10.3087 * -0.254864 -2.83778 10.3087 -0.220091 -2.47932 10.3087 * -0.185318 -2.12085 10.3087 -0.150545 -3.97604 -142.837 * -0.115773 -8.94286 -142.837 -0.810000E-01 -5.98360 115.342 * -0.462273E-01 -2.93620 25.9176 -0.114545E-01 -2.03497 25.9176 * 0.233182E-01 -1.13374 25.9176 0.580909E-01 -0.232518 25.9176 * 0.928636E-01 0.718031 113.426 0.127636 3.01873 -0.413333 * 0.162409 3.00436 -0.413333 0.197182 2.98999 -0.413333 * 0.231955 2.97561 -0.413333 0.266727 2.96124 -0.413333 * 0.301500 2.94687 -0.413333 0.336273 5.01815 366.934 * 0.371045 17.7774 366.934 0.405818 8.21098 275.864 * 0.440591 17.8035 275.864 0.475364 6.74090 -848.922 * 0.510136 -0.176991 111.356 0.544909 3.69515 111.356 * 0.579682 7.56730 111.356 0.614455 9.26900 -98.2559 * 0.649227 5.85238 -98.2559 0.684000 3.01776 59.0427 * 0.718773 5.07083 59.0427 0.753545 7.12391 59.0427 * 0.788318 9.17699 59.0427 0.823091 11.2301 59.0427 * 0.857864 12.2572 3.17404 0.892636 -1.63310 -724.648 * 0.927409 -6.69569 -2.47182 0.962182 -6.78164 -2.47182 * 0.996955 -6.86759 -2.47182 1.03173 -6.95354 -2.47182 * 1.06650 -7.03949 -2.47182 1.10127 -1.04282 202.519 * 1.13605 5.99931 202.519 1.17082 12.9056 179.569 * 1.20559 19.1497 179.569 1.24036 19.9130 -204.683 * 1.27514 12.7956 -204.683 1.30991 5.67824 -204.683 * 1.34468 15.6896 316.235 1.37945 13.5906 -73.9486 * 1.41423 11.0192 -73.9486 1.44900 8.44777 -73.9486 * 1.48377 5.87638 -73.9486 1.51855 3.30498 -73.9486 * 1.55332 0.733589 -73.9486 1.58809 3.73970 274.844 * 1.62286 13.2968 274.844 1.65764 11.8088 -72.0872 * 1.69241 9.30214 -72.0872 1.72718 6.79547 -72.0872 * 1.76195 4.28880 -72.0872 1.79673 13.6725 472.662 * 1.83150 25.4827 -98.3919 1.86627 22.0614 -98.3919 * 1.90105 18.6400 -98.3919 1.93582 15.2187 -98.3919 * 1.97059 11.7973 -98.3919 2.00536 9.31200 490.416 * 2.04014 -8.00800 297.090 2.07491 2.32263 297.090 * 2.10968 17.1897 -49.3888 2.14445 15.4723 -49.3888 * 2.17923 13.7549 -49.3888 2.21400 10.8975 -177.484 * 2.24877 4.72590 -177.484 2.28355 4.47465 116.396 * 2.31832 8.93565 154.985 2.35309 14.3249 154.985 * 2.38786 6.41016 -453.513 2.42264 23.3897 -87.1660 * 2.45741 20.3587 -87.1660 2.49218 17.3277 -87.1660 * 2.52695 14.2967 -87.1660 2.56173 11.2657 -87.1660 * 2.59650 11.5279 802.902 2.63127 32.0470 -149.147 * 2.66605 26.8608 -149.147 2.70082 21.6745 -149.147 * 2.73559 16.4882 -149.147 2.77036 11.3020 -149.147 * 2.80514 6.11573 -149.147 2.83991 10.1037 167.108 * 2.87468 15.9145 167.108 2.90945 13.4396 -254.460 * 2.94423 4.59133 -254.460 2.97900 9.76446 13.7406 * 3.01377 10.2423 13.7406 3.04855 10.7201 13.7406 * 3.08332 11.1979 13.7406 3.11809 12.3944 374.729 * 3.15286 23.4499 174.524 3.18764 26.0499 -97.8237 * 3.22241 22.6483 -97.8237 3.25718 20.5441 -32.5650 * 3.29195 19.4118 -32.5650 3.32673 18.2794 -32.5650 * 3.36150 17.1470 -32.5650 3.39627 16.0147 -32.5650 * 3.43105 16.2987 65.4860 3.46582 18.5758 65.4860 * 3.50059 20.8529 65.4860 3.53536 23.1301 65.4860 * 3.57014 25.4072 65.4860 3.60491 27.6843 65.4860 * 3.63968 28.2660 1.70238 3.67445 21.9916 60.2056 * 3.70923 24.0851 60.2056 3.74400 26.1787 60.2056 * 3.77877 14.1560 -416.614 3.81355 22.8095 -506.477 * 3.84832 14.9175 18.3869 3.88309 18.3438 224.969 * 3.91786 22.0089 -100.777 3.95264 18.7144 20.0274 * 3.98741 19.4108 20.0274 4.02218 20.1072 20.0274 * 4.05695 20.8036 20.0274 4.09173 25.9739 207.006 * 4.12650 30.5610 91.9827 4.16127 32.5031 -133.465 * 4.19605 27.8622 -133.465 4.23082 23.2213 -133.465 * 4.26559 25.8217 -80.2380 4.30036 23.0316 -80.2380 * 4.33514 24.5915 272.371 4.36991 26.9720 32.8992 * 4.40468 28.1160 32.8992 4.43945 25.6122 -120.663 * 4.47423 21.4164 -120.663 4.50900 19.4434 120.951 * 4.54377 23.6492 120.951 4.57855 27.7515 64.8716 * 4.61332 30.0073 64.8716 4.64809 30.0532 -65.9609 * 4.68286 27.7595 -65.9609 4.71764 30.0191 243.015 * 4.75241 38.4693 243.015 4.78718 38.1140 -325.755 * 4.82195 26.7866 -325.755 4.85673 19.8232 -21.1629 * 4.89150 19.0873 -21.1629 TEST05 Overhauser spline interpolation. Problem 1 DeBoor example, Mars position X Y * 1250.50 1.39140 1255.50 1.38602 * 1260.50 1.37696 1265.50 1.36420 * 1270.50 1.34783 1275.50 1.32792 * 1280.50 1.30456 1285.50 1.27784 * 1290.50 1.24787 1295.50 1.21476 * 1300.50 1.17862 1305.50 1.13957 * 1310.50 1.09776 1315.50 1.05331 * 1320.50 1.00636 1325.50 0.957052 * 1330.50 0.905530 1335.50 0.852010 * 1340.50 0.796420 Problem 2 DeBoor example, roughly linear data X Y * 1.00000 0.00000 1.50000 0.228750 * 2.00000 0.600000 2.50000 1.21313 * 3.00000 1.77000 3.50000 1.83125 * 4.00000 1.92000 4.50000 2.61125 * 5.00000 3.31000 5.50000 3.43500 * 6.00000 3.52000 6.50000 4.02313 * 7.00000 4.59000 7.50000 4.98687 * 8.00000 5.31000 8.50000 5.51562 * 9.00000 5.79000 9.50000 6.44812 * 10.0000 7.06000 10.5000 7.26000 * 11.0000 7.17000 Problem 3 The pulse data, 0 0 0 0 0 1 0 0 0 0 0 X Y * 0.00000 0.00000 0.500000 0.00000 * 1.00000 0.00000 1.50000 0.00000 * 2.00000 0.00000 2.50000 0.00000 * 3.00000 0.00000 3.50000 -0.625000E-01 * 4.00000 0.00000 4.50000 0.562500 * 5.00000 1.00000 5.50000 0.562500 * 6.00000 0.00000 6.50000 -0.625000E-01 * 7.00000 0.00000 7.50000 0.00000 * 8.00000 0.00000 8.50000 0.00000 * 9.00000 0.00000 9.50000 0.00000 * 10.0000 0.00000 Problem 4 The jump data, 0 0 0 0 0 1/2 1 1 1 1 1 X Y * 0.00000 0.00000 0.500000 0.00000 * 1.00000 0.00000 1.50000 0.00000 * 2.00000 0.00000 2.50000 0.00000 * 3.00000 0.00000 3.50000 0.00000 * 4.00000 0.00000 4.49500 -6.12563 * 4.99000 0.00000 4.99500 0.249375 * 5.00000 0.500000 5.00500 0.750625 * 5.01000 1.00000 5.50500 7.12563 * 6.00000 1.00000 6.50000 1.00000 * 7.00000 1.00000 7.50000 1.00000 * 8.00000 1.00000 8.50000 1.00000 * 9.00000 1.00000 9.50000 1.00000 * 10.0000 1.00000 Problem 5 DeBoor's Titanium property data X Y * 595.000 0.644000 600.000 0.628250 * 605.000 0.622000 610.000 0.627938 * 615.000 0.638000 620.000 0.644313 * 625.000 0.649000 630.000 0.652000 * 635.000 0.652000 640.000 0.645250 * 645.000 0.639000 650.000 0.641000 * 655.000 0.646000 660.000 0.652250 * 665.000 0.657000 670.000 0.655000 * 675.000 0.652000 680.000 0.653875 * 685.000 0.655000 690.000 0.648500 * 695.000 0.644000 700.000 0.652813 * 705.000 0.663000 710.000 0.663875 * 715.000 0.663000 720.000 0.665000 * 725.000 0.668000 730.000 0.672313 * 735.000 0.676000 740.000 0.675875 * 745.000 0.676000 750.000 0.681438 * 755.000 0.686000 760.000 0.683188 * 765.000 0.679000 770.000 0.677750 * 775.000 0.678000 780.000 0.679750 * 785.000 0.683000 790.000 0.688500 * 795.000 0.694000 800.000 0.696500 * 805.000 0.699000 810.000 0.703562 * 815.000 0.710000 820.000 0.718625 * 825.000 0.730000 830.000 0.744687 * 835.000 0.763000 840.000 0.783625 * 845.000 0.812000 850.000 0.854000 * 855.000 0.907000 860.000 0.963188 * 865.000 1.04400 870.000 1.16450 * 875.000 1.33600 880.000 1.60875 * 885.000 1.88100 890.000 2.06494 * 895.000 2.16900 900.000 2.16981 * 905.000 2.07500 910.000 1.85481 * 915.000 1.59800 920.000 1.39313 * 925.000 1.21100 930.000 1.04994 * 935.000 0.916000 940.000 0.817187 * 945.000 0.746000 950.000 0.701188 * 955.000 0.672000 960.000 0.645625 * 965.000 0.627000 970.000 0.618687 * 975.000 0.615000 980.000 0.610313 * 985.000 0.607000 990.000 0.605812 * 995.000 0.606000 1000.00 0.607812 * 1005.00 0.609000 1010.00 0.606313 * 1015.00 0.603000 1020.00 0.601500 * 1025.00 0.601000 1030.00 0.602000 * 1035.00 0.603000 1040.00 0.601500 * 1045.00 0.601000 1050.00 0.606500 * 1055.00 0.611000 1060.00 0.606188 * 1065.00 0.601000 1070.00 0.602375 * 1075.00 0.608000 Problem 6 The Sawtooth data X Y * 0.00000 0.00000 0.250000 0.750000 * 0.500000 1.00000 0.750000 0.458333 * 1.00000 0.00000 1.12500 0.208333 * 1.25000 0.500000 1.37500 0.812500 * 1.50000 1.00000 1.62500 0.812500 * 1.75000 0.500000 1.87500 0.175000 * 2.00000 0.00000 2.08333 0.133333 * 2.16667 0.333333 2.25000 0.500000 * 2.33333 0.666667 2.41667 0.875000 * 2.50000 1.00000 2.58333 0.875000 * 2.66667 0.666667 2.75000 0.500000 * 2.83333 0.333333 2.91667 0.119048 * 3.00000 -0.555112E-16 3.06250 0.982143E-01 * 3.12500 0.250000 3.18750 0.375000 * 3.25000 0.500000 3.31250 0.625000 * 3.37500 0.750000 3.43750 0.906250 * 3.50000 1.00000 3.56250 0.906250 * 3.62500 0.750000 3.68750 0.625000 * 3.75000 0.500000 3.81250 0.375000 * 3.87500 0.250000 3.93750 0.902778E-01 * 4.00000 0.00000 4.05000 0.777778E-01 * 4.10000 0.200000 4.15000 0.300000 * 4.20000 0.400000 4.25000 0.500000 * 4.30000 0.600000 4.35000 0.700000 * 4.40000 0.800000 4.45000 0.925000 * 4.50000 1.00000 4.55000 0.925000 * 4.60000 0.800000 4.65000 0.700000 * 4.70000 0.600000 4.75000 0.500000 * 4.80000 0.400000 4.85000 0.300000 * 4.90000 0.200000 4.95000 0.100000 * 5.00000 0.00000 Problem 7 Concavity test data X Y * 0.00000 0.00000 0.500000E-01 0.556250 * 0.100000 0.900000 0.150000 0.984375 * 0.200000 0.950000 0.250000 0.978125 * 0.300000 0.900000 0.350000 0.500000 * 0.400000 0.100000 0.450000 0.250000E-01 * 0.500000 0.500000E-01 0.550000 0.437500E-01 * 0.600000 0.500000E-01 0.700000 0.718750E-01 * 0.800000 0.200000 0.900000 0.518750 * 1.00000 1.00000 Problem 8 Extrapolation test data X Y * 0.00000 0.00000 35.5000 0.812936 * 71.0000 7.75540 87.5000 13.0838 * 104.000 19.7062 119.500 26.6780 * 135.000 35.5379 140.000 39.1309 * 145.000 42.9154 152.500 48.9577 * 160.000 54.7752 170.500 60.4236 * 181.000 66.7587 187.000 72.4323 * 193.000 78.4929 199.000 83.9481 * 205.000 89.7683 210.000 95.6256 * 215.000 101.746 220.000 107.348 * 225.000 113.482 231.500 123.520 * 238.000 135.457 Problem 9 Sunspot data, 1700-1960. X Y * 1700.00 5.00000 1700.50 8.12500 * 1701.00 11.0000 1701.50 13.4375 * 1702.00 16.0000 1702.50 19.0000 * 1703.00 23.0000 1703.50 28.5625 * 1704.00 36.0000 1704.50 49.6250 * 1705.00 58.0000 1705.50 45.4375 * 1706.00 29.0000 1706.50 23.3125 * 1707.00 20.0000 1707.50 14.5625 * 1708.00 10.0000 1708.50 8.68750 * 1709.00 8.00000 1709.50 5.56250 * 1710.00 3.00000 1710.50 1.18750 * 1711.00 0.00000 1711.50 -0.312500 * 1712.00 0.00000 1712.50 0.437500 * 1713.00 2.00000 1713.50 5.62500 * 1714.00 11.0000 1714.50 18.3125 * 1715.00 27.0000 1715.50 37.0000 * 1716.00 47.0000 1716.50 56.4375 * 1717.00 63.0000 1717.50 63.8125 * 1718.00 60.0000 1718.50 50.0000 * 1719.00 39.0000 1719.50 32.3125 * 1720.00 28.0000 1720.50 26.5625 * 1721.00 26.0000 1721.50 24.5625 * 1722.00 22.0000 1722.50 15.6250 * 1723.00 11.0000 1723.50 14.1250 * 1724.00 21.0000 1724.50 28.7500 * 1725.00 40.0000 1725.50 57.4375 * 1726.00 78.0000 1726.50 103.562 * 1727.00 122.000 1727.50 117.125 * 1728.00 103.000 1728.50 88.4375 * 1729.00 73.0000 1729.50 58.8750 * 1730.00 47.0000 1730.50 40.8750 * 1731.00 35.0000 1731.50 22.6250 * 1732.00 11.0000 1732.50 5.81250 * 1733.00 5.00000 1733.50 9.00000 * 1734.00 16.0000 1734.50 23.4375 * 1735.00 34.0000 1735.50 52.4375 * 1736.00 70.0000 1736.50 75.8750 * 1737.00 81.0000 1737.50 97.3125 * 1738.00 111.000 1738.50 109.625 * 1739.00 101.000 1739.50 88.4375 * 1740.00 73.0000 1740.50 56.0000 * 1741.00 40.0000 1741.50 28.1875 * 1742.00 20.0000 1742.50 17.4375 * 1743.00 16.0000 1743.50 9.87500 * 1744.00 5.00000 1744.50 6.62500 * 1745.00 11.0000 1745.50 15.7500 * 1746.00 22.0000 1746.50 30.4375 * 1747.00 40.0000 1747.50 49.8188 * 1748.00 60.0000 1748.50 71.5438 * 1749.00 80.9000 1749.50 85.6875 * 1750.00 83.4000 1750.50 65.7000 * 1751.00 47.7000 1751.50 46.5875 * 1752.00 47.8000 1752.50 40.4125 * 1753.00 30.7000 1753.50 20.5438 * 1754.00 12.2000 1754.50 9.70625 * 1755.00 9.60000 1755.50 8.35000 * 1756.00 10.2000 1756.50 20.3875 * 1757.00 32.4000 1757.50 40.9875 * 1758.00 47.6000 1758.50 51.1938 * 1759.00 54.0000 1759.50 57.4125 * 1760.00 62.9000 1760.50 76.5000 * 1761.00 85.9000 1761.50 75.9938 * 1762.00 61.2000 1762.50 52.1500 * 1763.00 45.1000 1763.50 40.7125 * 1764.00 36.4000 1764.50 28.7000 * 1765.00 20.9000 1765.50 13.5312 * 1766.00 11.4000 1766.50 22.0062 * 1767.00 37.8000 1767.50 53.1812 * 1768.00 69.8000 1768.50 90.2812 * 1769.00 106.100 1769.50 106.919 * 1770.00 100.800 1770.50 91.8125 * 1771.00 81.6000 1771.50 74.8312 * 1772.00 66.5000 1772.50 49.9688 * 1773.00 34.8000 1773.50 32.1937 * 1774.00 30.6000 1774.50 17.7375 * 1775.00 7.00000 1775.50 7.38125 * 1776.00 19.8000 1776.50 53.0812 * 1777.00 92.5000 1777.50 129.775 * 1778.00 154.400 1778.50 146.587 * 1779.00 125.900 1779.50 104.613 * 1780.00 84.8000 1780.50 75.7312 * 1781.00 68.1000 1781.50 53.2375 * 1782.00 38.5000 1782.50 29.5875 * 1783.00 22.8000 1783.50 14.6500 * 1784.00 10.2000 1784.50 12.6875 * 1785.00 24.1000 1785.50 51.3000 * 1786.00 82.9000 1786.50 111.194 * 1787.00 132.000 1787.50 135.319 * 1788.00 130.900 1788.50 126.194 * 1789.00 118.100 1789.50 104.656 * 1790.00 89.9000 1790.50 76.9000 * 1791.00 66.6000 1791.50 62.6625 * 1792.00 60.0000 1792.50 53.4062 * 1793.00 46.9000 1793.50 44.3625 * 1794.00 41.0000 1794.50 31.1125 * 1795.00 21.3000 1795.50 18.0187 * 1796.00 16.0000 1796.50 11.0125 * 1797.00 6.40000 1797.50 4.48125 * 1798.00 4.10000 1798.50 4.82500 * 1799.00 6.80000 1799.50 9.60000 * 1800.00 14.5000 1800.50 24.0438 * 1801.00 34.0000 1801.50 40.8375 * 1802.00 45.0000 1802.50 44.4625 * 1803.00 43.1000 1803.50 45.5125 * 1804.00 47.5000 1804.50 46.0063 * 1805.00 42.2000 1805.50 35.9438 * 1806.00 28.1000 1806.50 18.3438 * 1807.00 10.1000 1807.50 8.32500 * 1808.00 8.10000 1808.50 5.33125 * 1809.00 2.50000 1809.50 0.812500 * 1810.00 0.00000 1810.50 0.318750 * 1811.00 1.40000 1811.50 2.83750 * 1812.00 5.00000 1812.50 8.71875 * 1813.00 12.2000 1813.50 12.1562 * 1814.00 13.9000 1814.50 24.1063 * 1815.00 35.4000 1815.50 42.2375 * 1816.00 45.8000 1816.50 44.7875 * 1817.00 41.1000 1817.50 35.6938 * 1818.00 30.1000 1818.50 26.8312 * 1819.00 23.9000 1819.50 19.9250 * 1820.00 15.6000 1820.50 10.7438 * 1821.00 6.60000 1821.50 4.87500 * 1822.00 4.00000 1822.50 2.31875 * 1823.00 1.80000 1823.50 4.50625 * 1824.00 8.50000 1824.50 11.7375 * 1825.00 16.6000 1825.50 26.1250 * 1826.00 36.3000 1826.50 43.2687 * 1827.00 49.6000 1827.50 57.5563 * 1828.00 64.2000 1828.50 66.2688 * 1829.00 67.0000 1829.50 70.5687 * 1830.00 70.9000 1830.50 60.8625 * 1831.00 47.8000 1831.50 37.3937 * 1832.00 27.5000 1832.50 16.4375 * 1833.00 8.50000 1833.50 6.93125 * 1834.00 13.2000 1834.50 31.3062 * 1835.00 56.9000 1835.50 90.8812 * 1836.00 121.500 1836.50 136.131 * 1837.00 138.300 1837.50 122.894 * 1838.00 103.200 1838.50 93.5750 * 1839.00 85.7000 1839.50 75.8000 * 1840.00 64.6000 1840.50 50.1125 * 1841.00 36.7000 1841.50 29.5500 * 1842.00 24.2000 1842.50 16.4000 * 1843.00 10.7000 1843.50 10.4375 * 1844.00 15.0000 1844.50 26.4813 * 1845.00 40.1000 1845.50 50.0563 * 1846.00 61.5000 1846.50 79.7000 * 1847.00 98.5000 1847.50 115.688 * 1848.00 124.700 1848.50 113.994 * 1849.00 96.3000 1849.50 79.8063 * 1850.00 66.6000 1850.50 64.3438 * 1851.00 64.5000 1851.50 60.1125 * 1852.00 54.1000 1852.50 47.0500 * 1853.00 39.0000 1853.50 29.7250 * 1854.00 20.6000 1854.50 12.6500 * 1855.00 6.70000 1855.50 3.48125 * 1856.00 4.30000 1856.50 11.3437 * 1857.00 22.7000 1857.50 37.4625 * 1858.00 54.8000 1858.50 76.1813 * 1859.00 93.8000 1859.50 98.4000 * 1860.00 95.8000 1860.50 87.7562 * 1861.00 77.2000 1861.50 67.9313 * 1862.00 59.1000 1862.50 50.2313 * 1863.00 44.0000 1863.50 45.5875 * 1864.00 47.0000 1864.50 39.8250 * 1865.00 30.5000 1865.50 22.9312 * 1866.00 16.3000 1866.50 9.01875 * 1867.00 7.30000 1867.50 19.6125 * 1868.00 37.6000 1868.50 53.6313 * 1869.00 74.0000 1869.50 110.512 * 1870.00 139.000 1870.50 129.762 * 1871.00 111.200 1871.50 106.875 * 1872.00 101.600 1872.50 84.6437 * 1873.00 66.2000 1873.50 54.9688 * 1874.00 44.7000 1874.50 29.8625 * 1875.00 17.0000 1875.50 12.3500 * 1876.00 11.3000 1876.50 12.0563 * 1877.00 12.4000 1877.50 7.80625 * 1878.00 3.40000 1878.50 2.49375 * 1879.00 6.00000 1879.50 17.9375 * 1880.00 32.3000 1880.50 44.6063 * 1881.00 54.3000 1881.50 58.1250 * 1882.00 59.7000 1882.50 62.0500 * 1883.00 63.7000 1883.50 64.5563 * 1884.00 63.5000 1884.50 59.5125 * 1885.00 52.2000 1885.50 38.8625 * 1886.00 25.4000 1886.50 17.9688 * 1887.00 13.1000 1887.50 9.21250 * 1888.00 6.80000 1888.50 6.10625 * 1889.00 6.30000 1889.50 4.88750 * 1890.00 7.10000 1890.50 19.0625 * 1891.00 35.6000 1891.50 55.3250 * 1892.00 73.0000 1892.50 81.8312 * 1893.00 85.1000 1893.50 83.1812 * 1894.00 78.0000 1894.50 71.9437 * 1895.00 64.0000 1895.50 53.0000 * 1896.00 41.8000 1896.50 32.5812 * 1897.00 26.2000 1897.50 26.3875 * 1898.00 26.7000 1898.50 19.5938 * 1899.00 12.1000 1899.50 10.3125 * 1900.00 9.50000 1900.50 5.79375 * 1901.00 2.70000 1901.50 2.21250 * 1902.00 5.00000 1902.50 13.7437 * 1903.00 24.4000 1903.50 33.0687 * 1904.00 42.0000 1904.50 54.4562 * 1905.00 63.5000 1905.50 59.4812 * 1906.00 53.8000 1906.50 58.1375 * 1907.00 62.0000 1907.50 56.0500 * 1908.00 48.5000 1908.50 46.9375 * 1909.00 43.9000 1909.50 31.7687 * 1910.00 18.6000 1910.50 10.7000 * 1911.00 5.70000 1911.50 3.98125 * 1912.00 3.60000 1912.50 1.85625 * 1913.00 1.40000 1913.50 3.00000 * 1914.00 9.60000 1914.50 28.4062 * 1915.00 47.4000 1915.50 51.6875 * 1916.00 57.1000 1916.50 82.5625 * 1917.00 103.900 1917.50 96.2375 * 1918.00 80.6000 1918.50 72.2687 * 1919.00 63.6000 1919.50 50.2563 * 1920.00 37.6000 1920.50 30.9688 * 1921.00 26.1000 1921.50 19.9562 * 1922.00 14.2000 1922.50 8.57500 * 1923.00 5.80000 1923.50 9.00000 * 1924.00 16.7000 1924.50 29.9562 * 1925.00 44.3000 1925.50 55.5063 * 1926.00 63.9000 1926.50 67.1250 * 1927.00 69.0000 1927.50 74.5250 * 1928.00 77.8000 1928.50 73.7250 * 1929.00 64.9000 1929.50 50.4000 * 1930.00 35.7000 1930.50 27.2563 * 1931.00 21.2000 1931.50 15.5813 * 1932.00 11.1000 1932.50 7.58125 * 1933.00 5.70000 1933.50 5.15000 * 1934.00 8.70000 1934.50 19.8625 * 1935.00 36.1000 1935.50 57.4438 * 1936.00 79.7000 1936.50 100.075 * 1937.00 114.400 1937.50 115.469 * 1938.00 109.600 1938.50 100.212 * 1939.00 88.8000 1939.50 78.2687 * 1940.00 67.8000 1940.50 57.3937 * 1941.00 47.5000 1941.50 38.6750 * 1942.00 30.6000 1942.50 22.8125 * 1943.00 16.3000 1943.50 10.5813 * 1944.00 9.60000 1944.50 17.2688 * 1945.00 33.2000 1945.50 60.6875 * 1946.00 92.6000 1946.50 126.769 * 1947.00 151.600 1947.50 147.738 * 1948.00 136.300 1948.50 137.719 * 1949.00 134.700 1949.50 110.106 * 1950.00 83.9000 1950.50 75.8438 * 1951.00 69.4000 1951.50 50.6437 * 1952.00 31.5000 1952.50 20.9250 * 1953.00 13.9000 1953.50 5.95000 * 1954.00 4.40000 1954.50 14.1250 * 1955.00 38.0000 1955.50 88.9188 * 1956.00 141.700 1956.50 172.769 * 1957.00 190.200 1957.50 192.144 * 1958.00 184.800 1958.50 174.481 * 1959.00 159.000 1959.50 138.262 * 1960.00 112.300 Problem 10 Y = 2 + 5*X + 10*N(0,1). X Y * -1.99350 -1.89180 -1.94095 -35.2745 * -1.88840 -8.62020 -1.88485 -2.82353 * -1.88130 -0.415200 -1.87995 -2.47618 * -1.87860 -4.69670 -1.87500 -4.73997 * -1.87140 -2.41440 -1.84110 -8.60927 * -1.81080 -21.8853 -1.73610 -24.7487 * -1.66140 -16.5097 -1.63025 -13.5024 * -1.59910 -10.4657 -1.52070 -7.32047 * -1.44230 -4.11500 -1.39320 1.73866 * -1.34410 6.56650 -1.25855 -18.8183 * -1.17300 -6.76490 -1.16525 1.02751 * -1.15750 8.82760 -1.07305 24.6484 * -0.988600 1.81090 -0.904100 9.65530 * -0.819600 9.64280 -0.798350 9.24076 * -0.777100 -0.616500 -0.773850 -4.52267 * -0.770600 -8.42130 -0.748800 -49.3417 * -0.727000 -16.4491 -0.725650 -8.02464 * -0.724300 -0.667000E-01 -0.723550 3.37492 * -0.722800 6.57130 -0.673150 56.7359 * -0.623500 -4.04360 -0.612900 -5.24408 * -0.602300 -6.41940 -0.383650 -3.08358 * -0.165000 -1.91140 -0.138350 -6.45606 * -0.111700 -9.52460 -0.843500E-01 -7.10014 * -0.570000E-01 -3.21540 0.176500E-01 -1.49184 * 0.923000E-01 0.654100 0.102750 1.83915 * 0.113200 3.02470 0.214450 -2.94489 * 0.315700 2.94100 0.325000 15.4711 * 0.334300 9.78480 0.334950 7.30446 * 0.335600 4.77130 0.359150 -5.99951 * 0.382700 22.0539 0.392300 14.7341 * 0.401900 7.13010 0.429450 14.3907 * 0.457000 22.3302 0.471800 10.5056 * 0.486600 -2.79790 0.545350 -5.65421 * 0.604100 10.2864 0.642200 6.84328 * 0.680300 2.79930 0.759900 6.29874 * 0.839500 12.1989 0.856450 13.7464 * 0.873400 12.3065 0.892450 -7.12485 * 0.911500 -15.3026 0.915250 -11.2272 * 0.919000 -6.67490 0.995300 11.6700 * 1.07160 -7.05210 1.11825 1.64995 * 1.16490 11.8429 1.19550 18.6319 * 1.22610 22.8325 1.26895 12.5529 * 1.31180 5.29120 1.33010 11.6235 * 1.34840 16.8654 1.35910 16.0035 * 1.36980 14.3045 1.47095 -1.19087 * 1.57210 -0.655300 1.59895 6.84978 * 1.62580 14.1038 1.70035 5.82268 * 1.77490 3.35560 1.79915 14.8538 * 1.82340 26.2797 1.89830 -32.9517 * 1.97320 11.5406 1.97580 20.2991 * 1.97840 28.2522 1.99030 25.8145 * 2.00220 7.76050 2.01265 12.5067 * 2.02310 18.0102 2.03145 148.719 * 2.03980 11.5710 2.03995 1.79850 * 2.04010 -8.01880 2.05790 -300.015 * 2.07570 2.55760 2.07905 10.3759 * 2.08240 18.5371 2.14375 52.2431 * 2.20510 12.4771 2.23425 6.38600 * 2.26340 2.12980 2.28550 3.91014 * 2.30760 7.27450 2.33680 14.6738 * 2.36600 16.3256 2.37955 8.57879 * 2.39310 4.03540 2.40530 12.4432 * 2.41750 23.8374 2.50515 16.8874 * 2.59280 8.55720 2.60815 20.8870 * 2.62350 33.2063 2.71720 33.1804 * 2.81090 5.25610 2.85035 13.1836 * 2.88980 18.4409 2.92295 4.48995 * 2.95610 1.57020 2.96150 5.46200 * 2.96690 9.59820 3.04150 17.6077 * 3.11610 11.6483 3.12955 16.8110 * 3.14300 21.7285 3.15895 25.3126 * 3.17490 27.2958 3.20610 25.5180 * 3.23730 21.1916 3.32695 16.1386 * 3.41660 15.3527 3.51485 21.7743 * 3.61310 28.2207 3.63830 40.1068 * 3.66350 28.3065 3.66520 24.9403 * 3.66690 21.5368 3.70775 7.90859 * 3.74860 26.4556 3.75080 25.6901 * 3.75300 24.8933 3.76960 13.9376 * 3.78620 11.0617 3.79415 20.0226 * 3.80210 28.6064 3.81595 24.3874 * 3.82980 14.5770 3.84970 12.8600 * 3.86960 15.3088 3.88735 19.5010 * 3.90510 23.2952 3.92800 21.8433 * 3.95090 18.6796 4.00935 16.4929 * 4.06780 21.0208 4.08580 24.7608 * 4.10380 28.4730 4.12975 31.8359 * 4.15570 33.2469 4.20065 22.5816 * 4.24560 21.2484 4.25100 23.9213 * 4.25640 26.5592 4.28960 25.6624 * 4.32280 21.2314 4.33155 23.5524 * 4.34030 25.9979 4.37800 29.7543 * 4.41570 28.4785 4.45775 22.9290 * 4.49980 18.3307 4.53825 22.1874 * 4.57670 27.6318 4.60395 29.9429 * 4.63120 31.1673 4.66705 28.0556 * 4.70290 26.4379 4.73730 35.9088 * 4.77170 43.1573 4.80705 32.6007 * 4.84240 20.1264 4.86695 18.0745 * 4.89150 19.0873 TEST06 Cubic spline interpolation. Problem 1 DeBoor example, Mars position X Y * 1250.50 1.39140 1255.50 1.38603 * 1260.50 1.37696 1265.50 1.36420 * 1270.50 1.34783 1275.50 1.32792 * 1280.50 1.30456 1285.50 1.27784 * 1290.50 1.24787 1295.50 1.21476 * 1300.50 1.17862 1305.50 1.13958 * 1310.50 1.09776 1315.50 1.05331 * 1320.50 1.00636 1325.50 0.957041 * 1330.50 0.905530 1335.50 0.851979 * 1340.50 0.796420 Problem 2 DeBoor example, roughly linear data X Y * 1.00000 0.00000 1.50000 0.147883 * 2.00000 0.600000 2.50000 1.27548 * 3.00000 1.77000 3.50000 1.80393 * 4.00000 1.92000 4.50000 2.60628 * 5.00000 3.31000 5.50000 3.46843 * 6.00000 3.52000 6.50000 3.96999 * 7.00000 4.59000 7.50000 5.04535 * 8.00000 5.31000 8.50000 5.47486 * 9.00000 5.79000 9.50000 6.42397 * 10.0000 7.06000 10.5000 7.33302 * 11.0000 7.17000 Problem 3 The pulse data, 0 0 0 0 0 1 0 0 0 0 0 X Y * 0.00000 0.00000 0.500000 0.490196E-02 * 1.00000 0.00000 1.50000 -0.980392E-02 * 2.00000 0.00000 2.50000 0.343137E-01 * 3.00000 0.00000 3.50000 -0.127451 * 4.00000 0.00000 4.50000 0.600490 * 5.00000 1.00000 5.50000 0.600490 * 6.00000 0.00000 6.50000 -0.127451 * 7.00000 0.00000 7.50000 0.343137E-01 * 8.00000 0.00000 8.50000 -0.980392E-02 * 9.00000 0.00000 9.50000 0.490196E-02 * 10.0000 0.00000 Problem 4 The jump data, 0 0 0 0 0 1/2 1 1 1 1 1 X Y * 0.00000 0.00000 0.500000 -0.811346E-01 * 1.00000 0.00000 1.50000 0.162269 * 2.00000 0.00000 2.50000 -0.567942 * 3.00000 0.00000 3.50000 2.10950 * 4.00000 0.00000 4.49500 -7.76284 * 4.99000 0.00000 4.99500 0.248920 * 5.00000 0.500000 5.00500 0.751080 * 5.01000 1.00000 5.50500 8.76284 * 6.00000 1.00000 6.50000 -1.10950 * 7.00000 1.00000 7.50000 1.56794 * 8.00000 1.00000 8.50000 0.837731 * 9.00000 1.00000 9.50000 1.08113 * 10.0000 1.00000 Problem 5 DeBoor's Titanium property data X Y * 595.000 0.644000 600.000 0.626793 * 605.000 0.622000 610.000 0.628164 * 615.000 0.638000 620.000 0.644675 * 625.000 0.649000 630.000 0.652511 * 635.000 0.652000 640.000 0.645281 * 645.000 0.639000 650.000 0.639864 * 655.000 0.646000 660.000 0.653263 * 665.000 0.657000 670.000 0.654584 * 675.000 0.652000 680.000 0.654400 * 685.000 0.655000 690.000 0.648067 * 695.000 0.644000 700.000 0.652333 * 705.000 0.663000 710.000 0.664977 * 715.000 0.663000 720.000 0.664011 * 725.000 0.668000 730.000 0.672980 * 735.000 0.676000 740.000 0.675444 * 745.000 0.676000 750.000 0.681492 * 755.000 0.686000 760.000 0.683711 * 765.000 0.679000 770.000 0.677287 * 775.000 0.678000 780.000 0.679639 * 785.000 0.683000 790.000 0.688656 * 795.000 0.694000 800.000 0.696736 * 805.000 0.699000 810.000 0.703400 * 815.000 0.710000 820.000 0.718538 * 825.000 0.730000 830.000 0.745198 * 835.000 0.763000 840.000 0.783294 * 845.000 0.812000 850.000 0.854375 * 855.000 0.907000 860.000 0.967208 * 865.000 1.04400 870.000 1.15442 * 875.000 1.33600 880.000 1.60611 * 885.000 1.88100 890.000 2.07163 * 895.000 2.16900 900.000 2.17749 * 905.000 2.07500 910.000 1.85478 * 915.000 1.59800 920.000 1.38578 * 925.000 1.21100 930.000 1.05186 * 935.000 0.916000 940.000 0.814898 * 945.000 0.746000 950.000 0.702172 * 955.000 0.672000 960.000 0.646039 * 965.000 0.627000 970.000 0.618420 * 975.000 0.615000 980.000 0.610904 * 985.000 0.607000 990.000 0.605339 * 995.000 0.606000 1000.00 0.608116 * 1005.00 0.609000 1010.00 0.606571 * 1015.00 0.603000 1020.00 0.600976 * 1025.00 0.601000 1030.00 0.602524 * 1035.00 0.603000 1040.00 0.600928 * 1045.00 0.601000 1050.00 0.606765 * 1055.00 0.611000 1060.00 0.607014 * 1065.00 0.601000 1070.00 0.600806 * 1075.00 0.608000 Problem 6 The Sawtooth data X Y * 0.00000 0.00000 0.250000 0.927655 * 0.500000 1.00000 0.750000 0.394689 * 1.00000 0.00000 1.12500 0.167009 * 1.25000 0.500000 1.37500 0.839404 * 1.50000 1.00000 1.62500 0.850375 * 1.75000 0.500000 1.87500 0.134096 * 2.00000 0.00000 2.08333 0.131345 * 2.16667 0.333333 2.25000 0.496036 * 2.33333 0.666667 2.41667 0.884509 * 2.50000 1.00000 2.58333 0.882595 * 2.66667 0.666667 2.75000 0.501777 * 2.83333 0.333333 2.91667 0.110298 * 3.00000 0.00000 3.06250 0.895875E-01 * 3.12500 0.250000 3.18750 0.387114 * 3.25000 0.500000 3.31250 0.611956 * 3.37500 0.750000 3.43750 0.915063 * 3.50000 1.00000 3.56250 0.915292 * 3.62500 0.750000 3.68750 0.611267 * 3.75000 0.500000 3.81250 0.389639 * 3.87500 0.250000 3.93750 0.801769E-01 * 4.00000 0.00000 4.05000 0.721362E-01 * 4.10000 0.200000 4.15000 0.306900 * 4.20000 0.400000 4.25000 0.500264 * 4.30000 0.600000 4.35000 0.692046 * 4.40000 0.800000 4.45000 0.931554 * 4.50000 1.00000 4.55000 0.931738 * 4.60000 0.800000 4.65000 0.691493 * 4.70000 0.600000 4.75000 0.502290 * 4.80000 0.400000 4.85000 0.299346 * 4.90000 0.200000 4.95000 0.100327 * 5.00000 0.00000 Problem 7 Concavity test data X Y * 0.00000 0.00000 0.500000E-01 0.591250 * 0.100000 0.900000 0.150000 0.961249 * 0.200000 0.950000 0.250000 0.995003 * 0.300000 0.900000 0.350000 0.502489 * 0.400000 0.100000 0.450000 -0.495861E-02 * 0.500000 0.500000E-01 0.550000 0.673455E-01 * 0.600000 0.500000E-01 0.700000 0.615748E-01 * 0.800000 0.200000 0.900000 0.509838 * 1.00000 1.00000 Problem 8 Extrapolation test data X Y * 0.00000 0.00000 35.5000 0.617949 * 71.0000 7.75540 87.5000 13.2257 * 104.000 19.7062 119.500 26.6483 * 135.000 35.5379 140.000 39.0471 * 145.000 42.9154 152.500 49.1626 * 160.000 54.7752 170.500 60.2921 * 181.000 66.7587 187.000 72.4146 * 193.000 78.4929 199.000 83.9544 * 205.000 89.7683 210.000 95.6326 * 215.000 101.746 220.000 107.445 * 225.000 113.482 231.500 123.250 * 238.000 135.457 Problem 9 Sunspot data, 1700-1960. X Y * 1700.00 5.00000 1700.50 8.24884 * 1701.00 11.0000 1701.50 13.3773 * 1702.00 16.0000 1702.50 19.3669 * 1703.00 23.0000 1703.50 27.1552 * 1704.00 36.0000 1704.50 50.8874 * 1705.00 58.0000 1705.50 46.0451 * 1706.00 29.0000 1706.50 22.0573 * 1707.00 20.0000 1707.50 15.1009 * 1708.00 10.0000 1708.50 8.41414 * 1709.00 8.00000 1709.50 5.86754 * 1710.00 3.00000 1710.50 0.990688 * 1711.00 0.00000 1711.50 -0.205296 * 1712.00 0.00000 1712.50 0.455495 * 1713.00 2.00000 1713.50 5.50831 * 1714.00 11.0000 1714.50 18.2612 * 1715.00 27.0000 1715.50 36.8217 * 1716.00 47.0000 1716.50 56.4520 * 1717.00 63.0000 1717.50 64.4955 * 1718.00 60.0000 1718.50 49.9411 * 1719.00 39.0000 1719.50 31.7402 * 1720.00 28.0000 1720.50 26.4732 * 1721.00 26.0000 1721.50 25.2419 * 1722.00 22.0000 1722.50 15.4342 * 1723.00 11.0000 1723.50 13.7712 * 1724.00 21.0000 1724.50 29.2310 * 1725.00 40.0000 1725.50 55.8047 * 1726.00 78.0000 1726.50 104.675 * 1727.00 122.000 1727.50 118.370 * 1728.00 103.000 1728.50 87.5966 * 1729.00 73.0000 1729.50 58.3689 * 1730.00 47.0000 1730.50 41.1778 * 1731.00 35.0000 1731.50 23.1701 * 1732.00 11.0000 1732.50 4.89200 * 1733.00 5.00000 1733.50 9.63693 * 1734.00 16.0000 1734.50 22.5603 * 1735.00 34.0000 1735.50 53.2469 * 1736.00 70.0000 1736.50 75.5769 * 1737.00 81.0000 1737.50 96.6953 * 1738.00 111.000 1738.50 111.017 * 1739.00 101.000 1739.50 87.9879 * 1740.00 73.0000 1740.50 56.1566 * 1741.00 40.0000 1741.50 27.3857 * 1742.00 20.0000 1742.50 17.9258 * 1743.00 16.0000 1743.50 10.0363 * 1744.00 5.00000 1744.50 6.17897 * 1745.00 11.0000 1745.50 15.9978 * 1746.00 22.0000 1746.50 30.3298 * 1747.00 40.0000 1747.50 49.8081 * 1748.00 60.0000 1748.50 70.8004 * 1749.00 80.9000 1749.50 87.5030 * 1750.00 83.4000 1750.50 65.0127 * 1751.00 47.7000 1751.50 45.4462 * 1752.00 47.8000 1752.50 42.0275 * 1753.00 30.7000 1753.50 19.6188 * 1754.00 12.2000 1754.50 10.0097 * 1755.00 9.60000 1755.50 8.12986 * 1756.00 10.2000 1756.50 19.9708 * 1757.00 32.4000 1757.50 41.6118 * 1758.00 47.6000 1758.50 51.6070 * 1759.00 54.0000 1759.50 55.9725 * 1760.00 62.9000 1760.50 77.2779 * 1761.00 85.9000 1761.50 77.1161 * 1762.00 61.2000 1762.50 50.6704 * 1763.00 45.1000 1763.50 41.1022 * 1764.00 36.4000 1764.50 29.4957 * 1765.00 20.9000 1765.50 12.7150 * 1766.00 11.4000 1766.50 21.7818 * 1767.00 37.8000 1767.50 52.9452 * 1768.00 69.8000 1768.50 90.4749 * 1769.00 106.100 1769.50 108.193 * 1770.00 100.800 1770.50 90.5164 * 1771.00 81.6000 1771.50 75.7167 * 1772.00 66.5000 1772.50 49.3542 * 1773.00 34.8000 1773.50 32.1290 * 1774.00 30.6000 1774.50 19.3423 * 1775.00 7.00000 1775.50 5.42689 * 1776.00 19.8000 1776.50 51.3876 * 1777.00 92.5000 1777.50 132.060 * 1778.00 154.400 1778.50 148.422 * 1779.00 125.900 1779.50 102.276 * 1780.00 84.8000 1780.50 76.0493 * 1781.00 68.1000 1781.50 53.6646 * 1782.00 38.5000 1782.50 29.2173 * 1783.00 22.8000 1783.50 15.4912 * 1784.00 10.2000 1784.50 11.5180 * 1785.00 24.1000 1785.50 50.2617 * 1786.00 82.9000 1786.50 112.835 * 1787.00 132.000 1787.50 135.610 * 1788.00 130.900 1788.50 125.688 * 1789.00 118.100 1789.50 105.249 * 1790.00 89.9000 1790.50 76.0028 * 1791.00 66.6000 1791.50 62.9396 * 1792.00 60.0000 1792.50 53.3136 * 1793.00 46.9000 1793.50 44.5933 * 1794.00 41.0000 1794.50 31.1882 * 1795.00 21.3000 1795.50 17.6287 * 1796.00 16.0000 1796.50 11.4593 * 1797.00 6.40000 1797.50 4.10918 * 1798.00 4.10000 1798.50 5.14150 * 1799.00 6.80000 1799.50 9.27481 * 1800.00 14.5000 1800.50 23.7593 * 1801.00 34.0000 1801.50 41.6006 * 1802.00 45.0000 1802.50 44.1632 * 1803.00 43.1000 1803.50 45.2215 * 1804.00 47.5000 1804.50 46.3257 * 1805.00 42.2000 1805.50 36.2630 * 1806.00 28.1000 1806.50 17.9348 * 1807.00 10.1000 1807.50 8.11043 * 1808.00 8.10000 1808.50 5.77351 * 1809.00 2.50000 1809.50 0.533046 * 1810.00 0.00000 1810.50 0.469309 * 1811.00 1.40000 1811.50 2.55222 * 1812.00 5.00000 1812.50 9.24682 * 1813.00 12.2000 1813.50 11.8230 * 1814.00 13.9000 1814.50 23.5487 * 1815.00 35.4000 1815.50 42.9696 * 1816.00 45.8000 1816.50 44.8978 * 1817.00 41.1000 1817.50 35.4642 * 1818.00 30.1000 1818.50 26.6579 * 1819.00 23.9000 1819.50 20.2416 * 1820.00 15.6000 1820.50 10.5255 * 1821.00 6.60000 1821.50 4.96881 * 1822.00 4.00000 1822.50 2.24924 * 1823.00 1.80000 1823.50 4.59673 * 1824.00 8.50000 1824.50 11.5514 * 1825.00 16.6000 1825.50 26.1229 * 1826.00 36.3000 1826.50 43.3072 * 1827.00 49.6000 1827.50 57.7109 * 1828.00 64.2000 1828.50 65.9365 * 1829.00 67.0000 1829.50 70.8054 * 1830.00 70.9000 1830.50 61.3043 * 1831.00 47.8000 1831.50 37.0525 * 1832.00 27.5000 1832.50 16.8983 * 1833.00 8.50000 1833.50 6.47926 * 1834.00 13.2000 1834.50 30.1221 * 1835.00 56.9000 1835.50 90.8197 * 1836.00 121.500 1836.50 138.437 * 1837.00 138.300 1837.50 122.371 * 1838.00 103.200 1838.50 92.2907 * 1839.00 85.7000 1839.50 76.9158 * 1840.00 64.6000 1840.50 49.6460 * 1841.00 36.7000 1841.50 29.4753 * 1842.00 24.2000 1842.50 16.9527 * 1843.00 10.7000 1843.50 9.51387 * 1844.00 15.0000 1844.50 26.9168 * 1845.00 40.1000 1845.50 50.2564 * 1846.00 61.5000 1846.50 78.3451 * 1847.00 98.5000 1847.50 116.963 * 1848.00 124.700 1848.50 115.228 * 1849.00 96.3000 1849.50 78.1392 * 1850.00 66.6000 1850.50 64.2030 * 1851.00 64.5000 1851.50 60.7612 * 1852.00 54.1000 1852.50 46.9272 * 1853.00 39.0000 1853.50 29.8299 * 1854.00 20.6000 1854.50 12.7032 * 1855.00 6.70000 1855.50 3.25735 * 1856.00 4.30000 1856.50 11.3049 * 1857.00 22.7000 1857.50 36.8355 * 1858.00 54.8000 1858.50 76.4279 * 1859.00 93.8000 1859.50 99.4903 * 1860.00 95.8000 1860.50 87.2108 * 1861.00 77.2000 1861.50 68.1539 * 1862.00 59.1000 1862.50 49.5112 * 1863.00 44.0000 1863.50 45.7387 * 1864.00 47.0000 1864.50 40.3588 * 1865.00 30.5000 1865.50 23.1760 * 1866.00 16.3000 1866.50 8.27460 * 1867.00 7.30000 1867.50 20.0881 * 1868.00 37.6000 1868.50 51.7481 * 1869.00 74.0000 1869.50 112.057 * 1870.00 139.000 1870.50 130.999 * 1871.00 111.200 1871.50 105.223 * 1872.00 101.600 1872.50 85.5611 * 1873.00 66.2000 1873.50 54.4457 * 1874.00 44.7000 1874.50 30.3186 * 1875.00 17.0000 1875.50 11.3548 * 1876.00 11.3000 1876.50 12.7622 * 1877.00 12.4000 1877.50 8.28376 * 1878.00 3.40000 1878.50 1.69021 * 1879.00 6.00000 1879.50 17.5679 * 1880.00 32.3000 1880.50 45.3632 * 1881.00 54.3000 1881.50 58.1670 * 1882.00 59.7000 1882.50 61.7190 * 1883.00 63.7000 1883.50 64.4571 * 1884.00 63.5000 1884.50 60.1400 * 1885.00 52.2000 1885.50 38.7577 * 1886.00 25.4000 1886.50 17.5042 * 1887.00 13.1000 1887.50 9.28796 * 1888.00 6.80000 1888.50 6.51894 * 1889.00 6.30000 1889.50 4.82378 * 1890.00 7.10000 1890.50 18.0109 * 1891.00 35.6000 1891.50 55.8075 * 1892.00 73.0000 1892.50 82.5092 * 1893.00 85.1000 1893.50 82.8933 * 1894.00 78.0000 1894.50 71.9552 * 1895.00 64.0000 1895.50 53.3986 * 1896.00 41.8000 1896.50 31.6505 * 1897.00 26.2000 1897.50 26.8371 * 1898.00 26.7000 1898.50 19.8263 * 1899.00 12.1000 1899.50 9.87011 * 1900.00 9.50000 1900.50 6.46822 * 1901.00 2.70000 1901.50 1.46950 * 1902.00 5.00000 1902.50 14.0288 * 1903.00 24.4000 1903.50 32.5279 * 1904.00 42.0000 1904.50 55.3220 * 1905.00 63.5000 1905.50 59.2716 * 1906.00 53.8000 1906.50 57.8292 * 1907.00 62.0000 1907.50 56.3365 * 1908.00 48.5000 1908.50 46.7247 * 1909.00 43.9000 1909.50 32.4897 * 1910.00 18.6000 1910.50 9.77882 * 1911.00 5.70000 1911.50 4.19495 * 1912.00 3.60000 1912.50 2.67886 * 1913.00 1.40000 1913.50 1.37711 * 1914.00 9.60000 1914.50 29.8127 * 1915.00 47.4000 1915.50 50.5596 * 1916.00 57.1000 1916.50 82.5738 * 1917.00 103.900 1917.50 98.0203 * 1918.00 80.6000 1918.50 70.8702 * 1919.00 63.6000 1919.50 50.7615 * 1920.00 37.6000 1920.50 30.3712 * 1921.00 26.1000 1921.50 20.6162 * 1922.00 14.2000 1922.50 8.45157 * 1923.00 5.80000 1923.50 8.42755 * 1924.00 16.7000 1924.50 29.8382 * 1925.00 44.3000 1925.50 56.3070 * 1926.00 63.9000 1926.50 66.7214 * 1927.00 69.0000 1927.50 74.1575 * 1928.00 77.8000 1928.50 74.7984 * 1929.00 64.9000 1929.50 49.9987 * 1930.00 35.7000 1930.50 26.8067 * 1931.00 21.2000 1931.50 15.8619 * 1932.00 11.1000 1932.50 7.78318 * 1933.00 5.70000 1933.50 5.04289 * 1934.00 8.70000 1934.50 19.3453 * 1935.00 36.1000 1935.50 57.0511 * 1936.00 79.7000 1936.50 100.763 * 1937.00 114.400 1937.50 116.147 * 1938.00 109.600 1938.50 99.7100 * 1939.00 88.8000 1939.50 78.1875 * 1940.00 67.8000 1940.50 57.4023 * 1941.00 47.5000 1941.50 38.6157 * 1942.00 30.6000 1942.50 23.1849 * 1943.00 16.3000 1943.50 10.6198 * 1944.00 9.60000 1944.50 16.7735 * 1945.00 33.2000 1945.50 58.9488 * 1946.00 92.6000 1946.50 129.256 * 1947.00 151.600 1947.50 147.288 * 1948.00 136.300 1948.50 137.715 * 1949.00 134.700 1949.50 110.415 * 1950.00 83.9000 1950.50 74.8125 * 1951.00 69.4000 1951.50 51.8475 * 1952.00 31.5000 1952.50 20.1099 * 1953.00 13.9000 1953.50 7.46279 * 1954.00 4.40000 1954.50 11.3389 * 1955.00 38.0000 1955.50 88.5315 * 1956.00 141.700 1956.50 175.497 * 1957.00 190.200 1957.50 191.541 * 1958.00 184.800 1958.50 174.051 * 1959.00 159.000 1959.50 138.493 * 1960.00 112.300 Problem 10 Y = 2 + 5*X + 10*N(0,1). X Y * -1.99350 -1.89180 -1.94095 -64.3600 * -1.88840 -8.62020 -1.88485 -1.64103 * -1.88130 -0.415200 -1.87995 -2.45499 * -1.87860 -4.69670 -1.87500 -5.69095 * -1.87140 -2.41440 -1.84110 1.01825 * -1.81080 -21.8853 -1.73610 -36.7255 * -1.66140 -16.5097 -1.63025 -11.9405 * -1.59910 -10.4657 -1.52070 -10.2611 * -1.44230 -4.11500 -1.39320 5.34699 * -1.34410 6.56650 -1.25855 -23.7795 * -1.17300 -6.76490 -1.16525 1.00361 * -1.15750 8.82760 -1.07305 31.1221 * -0.988600 1.81090 -0.904100 -2.42049 * -0.819600 9.64280 -0.798350 10.0538 * -0.777100 -0.616500 -0.773850 -3.96611 * -0.770600 -8.42130 -0.748800 -54.9097 * -0.727000 -16.4491 -0.725650 -7.89689 * -0.724300 -0.667000E-01 -0.723550 3.45887 * -0.722800 6.57130 -0.673150 58.1976 * -0.623500 -4.04360 -0.612900 -7.04321 * -0.602300 -6.41940 -0.383650 12.7809 * -0.165000 -1.91140 -0.138350 -6.99321 * -0.111700 -9.52460 -0.843500E-01 -7.19239 * -0.570000E-01 -3.21540 0.176500E-01 -1.97450 * 0.923000E-01 0.654100 0.102750 2.28934 * 0.113200 3.02470 0.214450 -52.5400 * 0.315700 2.94100 0.325000 19.8987 * 0.334300 9.78480 0.334950 7.31004 * 0.335600 4.77130 0.359150 -10.1961 * 0.382700 22.0539 0.392300 16.8822 * 0.401900 7.13010 0.429450 11.0445 * 0.457000 22.3302 0.471800 12.1808 * 0.486600 -2.79790 0.545350 -12.7117 * 0.604100 10.2864 0.642200 10.5316 * 0.680300 2.79930 0.759900 -3.79296 * 0.839500 12.1989 0.856450 17.1605 * 0.873400 12.3065 0.892450 -9.08146 * 0.911500 -15.3026 0.915250 -11.4286 * 0.919000 -6.67490 0.995300 20.4177 * 1.07160 -7.05210 1.11825 -3.59922 * 1.16490 11.8429 1.19550 20.9484 * 1.22610 22.8325 1.26895 10.3474 * 1.31180 5.29120 1.33010 11.6925 * 1.34840 16.8654 1.35910 16.4419 * 1.36980 14.3045 1.47095 -6.22436 * 1.57210 -0.655300 1.59895 7.99695 * 1.62580 14.1038 1.70035 0.618996 * 1.77490 3.35560 1.79915 18.6435 * 1.82340 26.2797 1.89830 -43.5325 * 1.97320 11.5406 1.97580 20.0921 * 1.97840 28.2522 1.99030 44.6399 * 2.00220 7.76050 2.01265 -53.0588 * 2.02310 18.0102 2.03145 189.248 * 2.03980 11.5710 2.03995 1.81023 * 2.04010 -8.01880 2.05790 -331.056 * 2.07570 2.55760 2.07905 18.2309 * 2.08240 18.5371 2.14375 6.54509 * 2.20510 12.4771 2.23425 7.52513 * 2.26340 2.12980 2.28550 2.30294 * 2.30760 7.27450 2.33680 17.9920 * 2.36600 16.3256 2.37955 7.78907 * 2.39310 4.03540 2.40530 11.6983 * 2.41750 23.8374 2.50515 22.8120 * 2.59280 8.55720 2.60815 20.4979 * 2.62350 33.2063 2.71720 33.8988 * 2.81090 5.25610 2.85035 15.5990 * 2.88980 18.4409 2.92295 2.70027 * 2.95610 1.57020 2.96150 5.38285 * 2.96690 9.59820 3.04150 19.4701 * 3.11610 11.6483 3.12955 16.4660 * 3.14300 21.7285 3.15895 25.7618 * 3.17490 27.2958 3.20610 25.3665 * 3.23730 21.1916 3.32695 18.8246 * 3.41660 15.3527 3.51485 -1.22855 * 3.61310 28.2207 3.63830 45.3483 * 3.66350 28.3065 3.66520 24.9330 * 3.66690 21.5368 3.70775 6.39779 * 3.74860 26.4556 3.75080 25.8259 * 3.75300 24.8933 3.76960 12.7171 * 3.78620 11.0617 3.79415 20.0702 * 3.80210 28.6064 3.81595 26.2864 * 3.82980 14.5770 3.84970 9.76755 * 3.86960 15.3088 3.88735 20.5448 * 3.90510 23.2952 3.92800 22.1749 * 3.95090 18.6796 4.00935 15.0775 * 4.06780 21.0208 4.08580 24.5863 * 4.10380 28.4730 4.12975 33.1548 * 4.15570 33.2469 4.20065 20.5026 * 4.24560 21.2484 4.25100 23.9744 * 4.25640 26.5592 4.28960 26.1515 * 4.32280 21.2314 4.33155 23.2634 * 4.34030 25.9979 4.37800 31.3545 * 4.41570 28.4785 4.45775 21.9258 * 4.49980 18.3307 4.53825 21.5519 * 4.57670 27.6318 4.60395 30.8684 * 4.63120 31.1673 4.66705 26.7853 * 4.70290 26.4379 4.73730 36.4034 * 4.77170 43.1573 4.80705 33.9285 * 4.84240 20.1264 4.86695 16.3652 * 4.89150 19.0873 TEST07 Plot an Overhauser spline interpolant for problem 7. Data values stored in "test07_data.txt". Approximant values stored in "test07_approx.txt". TEST08 Plot a cubic spline interpolant for problem 7. Data values stored in "test08_data.txt". Approximant values stored in "test08_approx.txt". TEST09 B spline approximation. Problem 1 DeBoor example, Mars position X Y * 1250.50 1.39140 1255.50 1.38387 * 1260.50 1.37451 1265.50 1.36179 * 1270.50 1.34547 1275.50 1.32562 * 1280.50 1.30232 1285.50 1.27567 * 1290.50 1.24578 1295.50 1.21274 * 1300.50 1.17668 1305.50 1.13773 * 1310.50 1.09600 1315.50 1.05164 * 1320.50 1.00479 1325.50 0.955576 * 1330.50 0.904150 1335.50 0.850803 * 1340.50 0.796420 Problem 2 DeBoor example, roughly linear data X Y * 1.00000 0.00000 1.50000 0.311875 * 2.00000 0.695000 2.50000 1.17563 * 3.00000 1.60000 3.50000 1.84958 * 4.00000 2.12667 4.50000 2.61625 * 5.00000 3.11333 5.50000 3.40833 * 6.00000 3.66333 6.50000 4.06562 * 7.00000 4.53167 7.50000 4.93771 * 8.00000 5.27000 8.50000 5.56146 * 9.00000 5.92167 9.50000 6.41729 * 10.0000 6.86667 10.5000 7.09083 * 11.0000 7.17000 Problem 3 The pulse data, 0 0 0 0 0 1 0 0 0 0 0 X Y * 0.00000 0.00000 0.500000 0.00000 * 1.00000 0.00000 1.50000 0.00000 * 2.00000 0.00000 2.50000 0.00000 * 3.00000 0.00000 3.50000 0.208333E-01 * 4.00000 0.166667 4.50000 0.479167 * 5.00000 0.666667 5.50000 0.479167 * 6.00000 0.166667 6.50000 0.208333E-01 * 7.00000 0.00000 7.50000 0.00000 * 8.00000 0.00000 8.50000 0.00000 * 9.00000 0.00000 9.50000 0.00000 * 10.0000 0.00000 Problem 4 The jump data, 0 0 0 0 0 1/2 1 1 1 1 1 X Y * 0.00000 0.00000 0.500000 0.00000 * 1.00000 0.00000 1.50000 0.00000 * 2.00000 0.00000 2.50000 0.00000 * 3.00000 0.00000 3.50000 0.00000 * 4.00000 0.00000 4.49500 0.104167E-01 * 4.99000 0.833333E-01 4.99500 0.260417 * 5.00000 0.500000 5.00500 0.739583 * 5.01000 0.916667 5.50500 0.989583 * 6.00000 1.00000 6.50000 1.00000 * 7.00000 1.00000 7.50000 1.00000 * 8.00000 1.00000 8.50000 1.00000 * 9.00000 1.00000 9.50000 1.00000 * 10.0000 1.00000 Problem 5 DeBoor's Titanium property data X Y * 595.000 0.644000 600.000 0.633792 * 605.000 0.628333 610.000 0.630687 * 615.000 0.637167 620.000 0.643229 * 625.000 0.647667 630.000 0.650000 * 635.000 0.649333 640.000 0.645583 * 645.000 0.642333 650.000 0.643000 * 655.000 0.646667 660.000 0.651250 * 665.000 0.654333 670.000 0.654333 * 675.000 0.653333 680.000 0.653375 * 685.000 0.652667 690.000 0.649833 * 695.000 0.649000 700.000 0.653729 * 705.000 0.659833 710.000 0.662708 * 715.000 0.663833 720.000 0.665667 * 725.000 0.668500 730.000 0.671896 * 735.000 0.674667 740.000 0.676042 * 745.000 0.677667 750.000 0.680854 * 755.000 0.683167 760.000 0.682271 * 765.000 0.680000 770.000 0.678750 * 775.000 0.679000 780.000 0.680750 * 785.000 0.684000 790.000 0.688500 * 795.000 0.693000 800.000 0.696500 * 805.000 0.700000 810.000 0.704813 * 815.000 0.711500 820.000 0.720458 * 825.000 0.732167 830.000 0.747104 * 835.000 0.765667 840.000 0.788792 * 845.000 0.819667 850.000 0.861333 * 855.000 0.914000 860.000 0.979604 * 865.000 1.06983 870.000 1.19850 * 875.000 1.37817 880.000 1.60842 * 885.000 1.83817 890.000 2.01169 * 895.000 2.10533 900.000 2.10606 * 905.000 2.01117 910.000 1.83040 * 915.000 1.61300 920.000 1.40829 * 925.000 1.22633 930.000 1.06802 * 935.000 0.936833 940.000 0.835604 * 945.000 0.762000 950.000 0.711604 * 955.000 0.676833 960.000 0.650792 * 965.000 0.632500 970.000 0.621771 * 975.000 0.615667 980.000 0.611229 * 985.000 0.608167 990.000 0.606729 * 995.000 0.606667 1000.00 0.607396 * 1005.00 0.607500 1010.00 0.605896 * 1015.00 0.603667 1020.00 0.602167 * 1025.00 0.601667 1030.00 0.602000 * 1035.00 0.602333 1040.00 0.602167 * 1045.00 0.603000 1050.00 0.605833 * 1055.00 0.607667 1060.00 0.605938 * 1065.00 0.603833 1070.00 0.604854 * 1075.00 0.608000 Problem 6 The Sawtooth data X Y * 0.00000 0.00000 0.250000 0.458333 * 0.500000 0.666667 0.750000 0.489583 * 1.00000 0.250000 1.12500 0.281250 * 1.25000 0.500000 1.37500 0.729167 * 1.50000 0.833333 1.62500 0.729167 * 1.75000 0.500000 1.87500 0.267361 * 2.00000 0.138889 2.08333 0.184028 * 2.16667 0.333333 2.25000 0.500000 * 2.33333 0.666667 2.41667 0.819444 * 2.50000 0.888889 2.58333 0.819444 * 2.66667 0.666667 2.75000 0.500000 * 2.83333 0.333333 2.91667 0.178819 * 3.00000 0.972222E-01 3.06250 0.137153 * 3.12500 0.250000 3.18750 0.375000 * 3.25000 0.500000 3.31250 0.625000 * 3.37500 0.750000 3.43750 0.864583 * 3.50000 0.916667 3.56250 0.864583 * 3.62500 0.750000 3.68750 0.625000 * 3.75000 0.500000 3.81250 0.375000 * 3.87500 0.250000 3.93750 0.134375 * 4.00000 0.750000E-01 4.05000 0.109375 * 4.10000 0.200000 4.15000 0.300000 * 4.20000 0.400000 4.25000 0.500000 * 4.30000 0.600000 4.35000 0.700000 * 4.40000 0.800000 4.45000 0.891667 * 4.50000 0.933333 4.55000 0.891667 * 4.60000 0.800000 4.65000 0.700000 * 4.70000 0.600000 4.75000 0.500000 * 4.80000 0.400000 4.85000 0.300000 * 4.90000 0.200000 4.95000 0.100000 * 5.00000 0.00000 Problem 7 Concavity test data X Y * 0.00000 0.00000 0.500000E-01 0.432292 * 0.100000 0.758333 0.150000 0.905208 * 0.200000 0.933333 0.250000 0.907292 * 0.300000 0.775000 0.350000 0.500000 * 0.400000 0.225000 0.450000 0.916667E-01 * 0.500000 0.583333E-01 0.550000 0.541667E-01 * 0.600000 0.750000E-01 0.700000 0.141667 * 0.800000 0.308333 0.900000 0.613542 * 1.00000 1.00000 Problem 8 Extrapolation test data X Y * 0.00000 0.00000 35.5000 3.96510 * 71.0000 8.45463 87.5000 13.8991 * 104.000 20.3530 119.500 27.5268 * 135.000 34.1288 140.000 39.1439 * 145.000 43.6624 152.500 48.9412 * 160.000 54.7958 170.500 60.7643 * 181.000 66.7171 187.000 72.6110 * 193.000 78.4164 199.000 84.1357 * 205.000 89.8854 210.000 95.7668 * 215.000 101.706 220.000 107.822 * 225.000 115.189 231.500 124.683 * 238.000 135.457 Problem 9 Sunspot data, 1700-1960. X Y * 1700.00 5.00000 1700.50 7.97917 * 1701.00 10.8333 1701.50 13.5208 * 1702.00 16.3333 1702.50 19.6667 * 1703.00 24.0000 1703.50 29.8125 * 1704.00 37.5000 1704.50 46.1250 * 1705.00 49.5000 1705.50 42.8542 * 1706.00 32.3333 1706.50 24.8958 * 1707.00 19.8333 1707.50 15.1458 * 1708.00 11.3333 1708.50 9.10417 * 1709.00 7.50000 1709.50 5.47917 * 1710.00 3.33333 1710.50 1.60417 * 1711.00 0.500000 1711.50 0.104167 * 1712.00 0.333333 1712.50 1.18750 * 1713.00 3.16667 1713.50 6.79167 * 1714.00 12.1667 1714.50 19.2292 * 1715.00 27.6667 1715.50 37.0000 * 1716.00 46.3333 1716.50 54.5208 * 1717.00 59.8333 1717.50 60.7292 * 1718.00 57.0000 1718.50 49.3333 * 1719.00 40.6667 1719.50 33.8958 * 1720.00 29.5000 1720.50 27.1458 * 1721.00 25.6667 1721.50 23.8125 * 1722.00 20.8333 1722.50 16.7917 * 1723.00 14.5000 1723.50 16.6250 * 1724.00 22.5000 1724.50 31.0833 * 1725.00 43.1667 1725.50 59.5208 * 1726.00 79.0000 1726.50 98.8125 * 1727.00 111.500 1727.50 110.958 * 1728.00 101.167 1728.50 87.8542 * 1729.00 73.6667 1729.50 60.3750 * 1730.00 49.3333 1730.50 41.0417 * 1731.00 33.0000 1731.50 23.1250 * 1732.00 14.0000 1732.50 8.72917 * 1733.00 7.83333 1733.50 11.0000 * 1734.00 17.1667 1734.50 25.5208 * 1735.00 37.0000 1735.50 51.8542 * 1736.00 65.8333 1736.50 75.3750 * 1737.00 84.1667 1737.50 95.5625 * 1738.00 104.333 1738.50 104.792 * 1739.00 98.0000 1739.50 86.5208 * 1740.00 72.1667 1740.50 56.6667 * 1741.00 42.1667 1741.50 30.6042 * 1742.00 22.6667 1742.50 18.1875 * 1743.00 14.8333 1743.50 10.7083 * 1744.00 7.83333 1744.50 8.45833 * 1745.00 11.8333 1745.50 16.7500 * 1746.00 23.1667 1746.50 31.1875 * 1747.00 40.3333 1747.50 50.0604 * 1748.00 60.1500 1748.50 70.0854 * 1749.00 77.8333 1749.50 80.9708 * 1750.00 77.0333 1750.50 65.5000 * 1751.00 53.6667 1751.50 48.1375 * 1752.00 44.9333 1752.50 38.8625 * 1753.00 30.4667 1753.50 21.7521 * 1754.00 14.8500 1754.50 11.2979 * 1755.00 10.1333 1755.50 10.4167 * 1756.00 13.8000 1756.50 21.6042 * 1757.00 31.2333 1757.50 39.6708 * 1758.00 46.1333 1758.50 50.6688 * 1759.00 54.4167 1759.50 58.7958 * 1760.00 65.2500 1760.50 73.7000 * 1761.00 77.9500 1761.50 72.7354 * 1762.00 62.6333 1762.50 53.4833 * 1763.00 46.3333 1763.50 40.7625 * 1764.00 35.2667 1764.50 28.6333 * 1765.00 21.9000 1765.50 17.0229 * 1766.00 17.3833 1766.50 25.4646 * 1767.00 38.7333 1767.50 54.0063 * 1768.00 70.5167 1768.50 87.1729 * 1769.00 99.1667 1769.50 102.294 * 1770.00 98.4833 1770.50 90.9958 * 1771.00 82.2833 1771.50 73.7896 * 1772.00 63.7333 1772.50 50.8771 * 1773.00 39.3833 1773.50 32.8688 * 1774.00 27.3667 1774.50 19.1542 * 1775.00 13.0667 1775.50 15.4063 * 1776.00 29.7833 1776.50 57.1729 * 1777.00 90.7000 1777.50 121.342 * 1778.00 139.333 1778.50 138.004 * 1779.00 123.800 1779.50 105.596 * 1780.00 88.8667 1780.50 76.6896 * 1781.00 65.9500 1781.50 53.3208 * 1782.00 40.8167 1782.50 31.0042 * 1783.00 23.3167 1783.50 17.1167 * 1784.00 14.6167 1784.50 18.6375 * 1785.00 31.5833 1785.50 54.2333 * 1786.00 81.2833 1786.50 106.202 * 1787.00 123.633 1787.50 130.160 * 1788.00 128.950 1788.50 123.935 * 1789.00 115.533 1789.50 103.781 * 1790.00 90.7167 1790.50 78.7000 * 1791.00 69.3833 1791.50 63.5125 * 1792.00 58.9167 1792.50 53.4646 * 1793.00 48.1000 1793.50 43.8125 * 1794.00 38.7000 1794.50 31.1625 * 1795.00 23.7000 1795.50 18.8604 * 1796.00 15.2833 1796.50 11.2625 * 1797.00 7.61667 1797.50 5.50625 * 1798.00 4.93333 1798.50 5.65833 * 1799.00 7.63333 1799.50 11.0000 * 1800.00 16.4667 1800.50 24.3188 * 1801.00 32.5833 1801.50 39.0542 * 1802.00 42.8500 1802.50 43.9125 * 1803.00 44.1500 1803.50 45.2292 * 1804.00 45.8833 1804.50 44.4646 * 1805.00 40.7333 1805.50 34.8854 * 1806.00 27.4500 1806.50 19.3521 * 1807.00 12.7667 1807.50 9.35833 * 1808.00 7.50000 1808.50 5.28958 * 1809.00 3.01667 1809.50 1.39583 * 1810.00 0.650000 1810.50 0.827083 * 1811.00 1.76667 1811.50 3.32083 * 1812.00 5.60000 1812.50 8.56042 * 1813.00 11.2833 1813.50 13.3479 * 1814.00 17.2000 1814.50 24.8312 * 1815.00 33.5500 1815.50 40.0542 * 1816.00 43.2833 1816.50 43.0042 * 1817.00 40.0500 1817.50 35.5688 * 1818.00 30.9000 1818.50 27.0562 * 1819.00 23.5500 1819.50 19.6917 * 1820.00 15.4833 1820.50 11.2188 * 1821.00 7.66667 1821.50 5.44167 * 1822.00 4.06667 1822.50 3.09375 * 1823.00 3.28333 1823.50 5.36458 * 1824.00 8.73333 1824.50 12.8208 * 1825.00 18.5333 1825.50 26.5583 * 1826.00 35.2333 1826.50 42.8438 * 1827.00 49.8167 1827.50 56.6813 * 1828.00 62.2333 1828.50 65.3771 * 1829.00 67.1833 1829.50 68.4104 * 1830.00 66.4000 1830.50 58.8458 * 1831.00 48.2667 1831.50 37.7354 * 1832.00 27.7167 1832.50 18.5208 * 1833.00 12.4500 1833.50 12.1563 * 1834.00 19.7000 1834.50 36.2979 * 1835.00 60.3833 1835.50 88.6396 * 1836.00 113.533 1836.50 127.823 * 1837.00 129.650 1837.50 120.035 * 1838.00 106.133 1838.50 94.7417 * 1839.00 85.1000 1839.50 74.9333 * 1840.00 63.4667 1840.50 50.8292 * 1841.00 39.2667 1841.50 30.7500 * 1842.00 24.0333 1842.50 17.8000 * 1843.00 13.6667 1843.50 13.6542 * 1844.00 18.4667 1844.50 27.9062 * 1845.00 39.4833 1845.50 51.0479 * 1846.00 64.1000 1846.50 80.1000 * 1847.00 96.7000 1847.50 110.238 * 1848.00 115.600 1848.50 109.335 * 1849.00 96.0833 1849.50 81.9979 * 1850.00 71.2000 1850.50 65.9521 * 1851.00 63.1167 1851.50 59.0292 * 1852.00 53.3167 1852.50 46.3833 * 1853.00 38.4500 1853.50 29.8250 * 1854.00 21.3500 1854.50 13.9833 * 1855.00 8.61667 1855.50 6.17292 * 1856.00 7.76667 1856.50 14.2188 * 1857.00 24.9833 1857.50 39.1792 * 1858.00 55.9500 1858.50 73.6729 * 1859.00 87.6333 1859.50 93.6000 * 1860.00 92.3667 1860.50 86.0812 * 1861.00 77.2833 1861.50 68.2229 * 1862.00 59.6000 1862.50 51.9896 * 1863.00 47.0167 1863.50 45.4708 * 1864.00 43.7500 1864.50 38.3917 * 1865.00 30.8833 1865.50 23.5563 * 1866.00 17.1667 1866.50 12.7271 * 1867.00 13.8500 1867.50 23.3958 * 1868.00 38.6167 1868.50 56.5229 * 1869.00 78.7667 1869.50 105.162 * 1870.00 123.533 1870.50 123.546 * 1871.00 114.233 1871.50 106.242 * 1872.00 97.3000 1872.50 83.6521 * 1873.00 68.5167 1873.50 55.6104 * 1874.00 43.6667 1874.50 31.1792 * 1875.00 20.6667 1875.50 14.7500 * 1876.00 12.4333 1876.50 11.7812 * 1877.00 10.7167 1877.50 7.93125 * 1878.00 5.33333 1878.50 5.43542 * 1879.00 9.95000 1879.50 19.5542 * 1880.00 31.5833 1880.50 42.8646 * 1881.00 51.5333 1881.50 56.6250 * 1882.00 59.4667 1882.50 61.5833 * 1883.00 63.0000 1883.50 63.2813 * 1884.00 61.6500 1884.50 57.2958 * 1885.00 49.6167 1885.50 38.7792 * 1886.00 27.8167 1886.50 19.6771 * 1887.00 14.1000 1887.50 10.1958 * 1888.00 7.76667 1888.50 6.69792 * 1889.00 6.51667 1889.50 7.30417 * 1890.00 11.7167 1890.50 22.1125 * 1891.00 37.0833 1891.50 53.9583 * 1892.00 68.7833 1892.50 78.1229 * 1893.00 81.9000 1893.50 81.0062 * 1894.00 76.8500 1894.50 70.6854 * 1895.00 62.6333 1895.50 52.8667 * 1896.00 42.9000 1896.50 34.4729 * 1897.00 28.8833 1897.50 26.4708 * 1898.00 24.1833 1898.50 19.3354 * 1899.00 14.1000 1899.50 10.9625 * 1900.00 8.80000 1900.50 6.20208 * 1901.00 4.21667 1901.50 4.39583 * 1902.00 7.85000 1902.50 15.0188 * 1903.00 24.1000 1903.50 33.2437 * 1904.00 42.6500 1904.50 52.1812 * 1905.00 58.3000 1905.50 58.3729 * 1906.00 56.7833 1906.50 57.8208 * 1907.00 58.3833 1907.50 54.9833 * 1908.00 49.9833 1908.50 45.9542 * 1909.00 40.4500 1909.50 31.0771 * 1910.00 20.6667 1910.50 12.6333 * 1911.00 7.50000 1911.50 4.87292 * 1912.00 3.58333 1912.50 2.71458 * 1913.00 3.13333 1913.50 6.33333 * 1914.00 14.5333 1914.50 28.5312 * 1915.00 42.7167 1915.50 52.4375 * 1916.00 63.2833 1916.50 79.8125 * 1917.00 92.2167 1917.50 90.9208 * 1918.00 81.6500 1918.50 72.0437 * 1919.00 62.1000 1919.50 50.7146 * 1920.00 40.0167 1920.50 32.1438 * 1921.00 26.0333 1921.50 20.2146 * 1922.00 14.7833 1922.50 10.4750 * 1923.00 9.01667 1923.50 12.0000 * 1924.00 19.4833 1924.50 30.6813 * 1925.00 42.9667 1925.50 53.6313 * 1926.00 61.4833 1926.50 66.2250 * 1927.00 69.6167 1927.50 73.0250 * 1928.00 74.1833 1928.50 70.5583 * 1929.00 62.1833 1929.50 50.2667 * 1930.00 38.1500 1930.50 28.8479 * 1931.00 21.9333 1931.50 16.3396 * 1932.00 11.8833 1932.50 8.67292 * 1933.00 7.10000 1933.50 7.88333 * 1934.00 12.7667 1934.50 23.2458 * 1935.00 38.8000 1935.50 58.0521 * 1936.00 78.2167 1936.50 96.0417 * 1937.00 107.817 1937.50 110.844 * 1938.00 106.933 1938.50 98.8625 * 1939.00 88.7667 1939.50 78.3104 * 1940.00 67.9167 1940.50 57.7354 * 1941.00 48.0667 1941.50 39.1750 * 1942.00 31.0333 1942.50 23.6625 * 1943.00 17.5667 1943.50 13.7396 * 1944.00 14.6500 1944.50 22.7771 * 1945.00 39.1667 1945.50 63.6375 * 1946.00 92.5333 1946.50 120.544 * 1947.00 139.217 1947.50 142.688 * 1948.00 138.583 1948.50 134.760 * 1949.00 126.500 1949.50 109.031 * 1950.00 89.9500 1950.50 76.9188 * 1951.00 65.5000 1951.50 50.3854 * 1952.00 34.8833 1952.50 23.2917 * 1953.00 15.2500 1953.50 10.2167 * 1954.00 11.5833 1954.50 23.5583 * 1955.00 49.6833 1955.50 90.1604 * 1956.00 132.500 1956.50 163.677 * 1957.00 181.217 1957.50 185.952 * 1958.00 181.400 1958.50 171.040 * 1959.00 155.517 1959.50 135.215 * 1960.00 112.300 Problem 10 Y = 2 + 5*X + 10*N(0,1). X Y * -1.99350 -1.89180 -1.94095 -4.94489 * -1.88840 -6.13130 -1.88485 -4.46672 * -1.88130 -2.49628 -1.87995 -2.67934 * -1.87860 -3.60273 -1.87500 -3.87200 * -1.87140 -6.03993 -1.84110 -12.0854 * -1.81080 -17.7442 -1.73610 -18.6659 * -1.66140 -16.3983 -1.63025 -13.4674 * -1.59910 -10.4146 -1.52070 -7.19374 * -1.44230 -3.39320 -1.39320 0.815706 * -1.34410 2.56435 -1.25855 0.311250E-02 * -1.17300 -1.94425 -1.16525 1.16291 * -1.15750 5.05940 -1.07305 5.15757 * -0.988600 4.28567 -0.904100 5.65930 * -0.819600 6.62760 -0.798350 4.18739 * -0.777100 -0.207417 -0.773850 -4.47241 * -0.770600 -8.45847 -0.748800 -11.9313 * -0.727000 -12.3807 -0.725650 -7.95236 * -0.724300 -1.69077 -0.723550 2.68986 * -0.722800 3.69582 -0.673150 1.07606 * -0.623500 -2.67042 -0.612900 -4.91644 * -0.602300 -5.27210 -0.383650 -4.27451 * -0.165000 -3.93160 -0.138350 -5.68047 * -0.111700 -7.20420 -0.843500E-01 -6.13078 * -0.570000E-01 -3.62202 0.176500E-01 -1.36270 * 0.923000E-01 0.404283 0.102750 1.75704 * 0.113200 2.61565 0.214450 3.07604 * 0.315700 4.09558 0.325000 6.26020 * 0.334300 7.80858 0.334950 7.49553 * 0.335600 8.48732 0.359150 13.2061 * 0.382700 16.6862 0.392300 14.5486 * 0.401900 12.1507 0.429450 14.5176 * 0.457000 15.6088 0.471800 9.72207 * 0.486600 3.57083 0.545350 4.11177 * 0.604100 6.85783 0.642200 6.46609 * 0.680300 5.61375 0.759900 7.65732 * 0.839500 10.6502 0.856450 11.4817 * 0.873400 7.68705 0.892450 -1.32055 * 0.911500 -9.26313 0.915250 -10.4214 * 0.919000 -8.17572 0.995300 -6.64960 * 1.07160 -3.84007 1.11825 2.63221 * 1.16490 10.5253 1.19550 16.5786 * 1.22610 18.0773 1.26895 14.0740 * 1.31180 10.1438 1.33010 11.3904 * 1.34840 14.5096 1.35910 15.0322 * 1.36980 12.2380 1.47095 7.18543 * 1.57210 4.29785 1.59895 6.81199 * 1.62580 9.85258 1.70035 8.89980 * 1.77490 8.96765 1.79915 14.7345 * 1.82340 20.0025 1.89830 18.7807 * 1.97320 16.7824 1.97580 19.7766 * 1.97840 22.0516 1.99030 17.8717 * 2.00220 12.8841 2.01265 13.1781 * 2.02310 15.2287 2.03145 14.1689 * 2.03980 9.37923 2.03995 2.13059 * 2.04010 -2.99110 2.05790 -1.98957 * 2.07570 3.45812 2.07905 10.2008 * 2.08240 14.8638 2.14375 14.9586 * 2.20510 11.7625 2.23425 7.53688 * 2.26340 4.71180 2.28550 5.10628 * 2.30760 7.92557 2.33680 11.4368 * 2.36600 12.7687 2.37955 10.4045 * 2.39310 9.38410 2.40530 13.8741 * 2.41750 17.9904 2.50515 16.2983 * 2.59280 15.2121 2.60815 20.6178 * 2.62350 24.4397 2.71720 18.9924 * 2.81090 12.1119 2.85035 12.0793 * 2.88980 13.4316 2.92295 9.89812 * 2.95610 5.71998 2.96150 5.97838 * 2.96690 8.60188 3.04150 10.6660 * 3.11610 12.9867 3.12955 16.7617 * 3.14300 20.9764 3.15895 24.1750 * 3.17490 25.3505 3.20610 24.0061 * 3.23730 21.2358 3.32695 18.6674 * 3.41660 18.4705 3.51485 21.9101 * 3.61310 26.0903 3.63830 27.8545 * 3.66350 27.1639 3.66520 25.0223 * 3.66690 23.4849 3.70775 24.1047 * 3.74860 25.3754 3.75080 25.2838 * 3.75300 22.8484 3.76960 18.3756 * 3.78620 16.2911 3.79415 19.8299 * 3.80210 23.3440 3.81595 21.2414 * 3.82980 17.0372 3.84970 15.4016 * 3.86960 16.5179 3.88735 19.1906 * 3.90510 21.1949 3.92800 20.8698 * 3.95090 19.8391 4.00935 20.1016 * 4.06780 21.8726 4.08580 24.7976 * 4.10380 28.0266 4.12975 30.4547 * 4.15570 30.4515 4.20065 27.2588 * 4.24560 24.1333 4.25100 24.0428 * 4.25640 24.7861 4.28960 23.8840 * 4.32280 22.9138 4.33155 23.7773 * 4.34030 25.6169 4.37800 26.9275 * 4.41570 26.3738 4.45775 23.5467 * 4.49980 21.5722 4.53825 23.2663 * 4.57670 26.6709 4.60395 29.1072 * 4.63120 29.7898 4.66705 29.0773 * 4.70290 30.0127 4.73730 34.4163 * 4.77170 36.5322 4.80705 31.2719 * 4.84240 23.7917 4.86695 20.0650 * 4.89150 19.0873 TEST10 Plot a B spline approximant for problem 7 Data values stored in "test10_data.txt". Approximant values stored in "test10_approx.txt". TEST11 Plot a beta spline approximant for problem 7 BETA1 = 100.000 BETA2 = 0.00000 Data values stored in "test11_data.txt". Approximant values stored in "test11_approx.txt". TEST12 Plot a Bernstein approximant for problem 5. Note that the Bernstein approximant requires equally spaced data! Data values stored in "test12_data.txt". Approximant values stored in "test12_approx.txt". TEST13 Plot a cubic spline interpolant for problem 5 Data values stored in "test13_data.txt". Interpolant values stored in "test13_approx.txt". TEST_APPROX_TEST Normal end of execution. 17 September 2021 11:53:49.663 PM