21 April 2020 02:34:38 PM TEST_APPROX_TEST C++ 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 * 1250.5 1.3914 1255.5 1.38606 * 1260.5 1.37696 1265.5 1.3642 * 1270.5 1.34783 1275.5 1.32792 * 1280.5 1.30456 1285.5 1.27784 * 1290.5 1.24787 1295.5 1.21476 * 1300.5 1.17862 1305.5 1.13958 * 1310.5 1.09776 1315.5 1.05331 * 1320.5 1.00636 1325.5 0.957057 * 1330.5 0.90553 1335.5 0.85192 * 1340.5 0.79642 Problem 2 DeBoor example, roughly linear data DATA_NUM = 11 Interpolating polynomial order = 11 * 1 0 1.5 -4.83067 * 2 0.6 2.5 2.3948 * 3 1.77 3.5 1.37568 * 4 1.92 4.5 2.78486 * 5 3.31 5.5 3.42747 * 6 3.52 6.5 3.9258 * 7 4.59 7.5 5.14001 * 8 5.31 8.5 5.32911 * 9 5.79 9.5 6.80032 * 10 7.06 10.5 5.07361 * 11 7.17 Problem 3 The pulse data, 0 0 0 0 0 1 0 0 0 0 0 DATA_NUM = 11 Interpolating polynomial order = 11 * 0 0 0.5 4.93352 * 1 0 1.5 -1.00154 * 2 0 2.5 0.412399 * 3 0 3.5 -0.320755 * 4 0 4.5 0.666183 * 5 1 5.5 0.666183 * 6 0 6.5 -0.320755 * 7 0 7.5 0.412399 * 8 1.16573e-14 8.5 -1.00154 * 9 2.6229e-14 9.5 4.93352 * 10 2.09832e-13 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 0 0.05 1.32484 * 0.1 0.9 0.15 0.752561 * 0.2 0.95 0.25 1.07856 * 0.3 0.9 0.35 0.489281 * 0.4 0.1 0.45 -0.0517323 * 0.5 0.05 0.55 0.190582 * 0.6 0.05 0.7 -1.36104 * 0.8 0.2 0.9 11.7975 * 1 1 Problem 8 Extrapolation test data DATA_NUM = 12 Interpolating polynomial order = 12 * 0 0 35.5 53263.6 * 71 7.7554 87.5 -365.169 * 104 19.7062 119.5 52.6291 * 135 35.5379 140 38.2108 * 145 42.9154 152.5 50.0208 * 160 54.7752 170.5 59.3723 * 181 66.7587 187 72.5336 * 193 78.4929 199 84.1117 * 205 89.7683 210 95.2479 * 215 101.746 220 108.479 * 225 113.482 231.5 116.128 * 238 135.457 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' * 1250.5 1.3914 -0.001444 1255.5 1.38418 -0.001444 * 1260.5 1.37696 -0.002913 1265.5 1.3624 -0.002913 * 1270.5 1.34783 -0.004327 1275.5 1.3262 -0.004327 * 1280.5 1.30456 -0.005669 1285.5 1.27622 -0.005669 * 1290.5 1.24787 -0.006925 1295.5 1.21325 -0.006925 * 1300.5 1.17862 -0.008086 1305.5 1.13819 -0.008086 * 1310.5 1.09776 -0.00914 1315.5 1.05206 -0.00914 * 1320.5 1.00636 -0.010083 1325.5 0.955945 -0.010083 * 1330.5 0.90553 -0.010911 1335.5 0.850975 -0.010911 * 1340.5 0.79642 -0.010911 Problem 2 DeBoor example, roughly linear data X Y Y' * 1 0 0.6 1.5 0.3 0.6 * 2 0.6 1.17 2.5 1.185 1.17 * 3 1.77 0.15 3.5 1.845 0.15 * 4 1.92 1.39 4.5 2.615 1.39 * 5 3.31 0.21 5.5 3.415 0.21 * 6 3.52 1.07 6.5 4.055 1.07 * 7 4.59 0.72 7.5 4.95 0.72 * 8 5.31 0.48 8.5 5.55 0.48 * 9 5.79 1.27 9.5 6.425 1.27 * 10 7.06 0.11 10.5 7.115 0.11 * 11 7.17 0.11 Problem 3 The pulse data, 0 0 0 0 0 1 0 0 0 0 0 X Y Y' * 0 0 0 0.5 0 0 * 1 0 0 1.5 0 0 * 2 0 0 2.5 0 0 * 3 0 0 3.5 0 0 * 4 0 1 4.5 0.5 1 * 5 1 -1 5.5 0.5 -1 * 6 0 0 6.5 0 0 * 7 0 0 7.5 0 0 * 8 0 0 8.5 0 0 * 9 0 0 9.5 0 0 * 10 0 0 Problem 4 The jump data, 0 0 0 0 0 1/2 1 1 1 1 1 X Y Y' * 0 0 0 0.416667 0 0 * 0.833333 0 0 1.25 0 0 * 1.66667 0 0 2.08333 0 0 * 2.5 0 0 2.91667 0 0 * 3.33333 0 0 3.75 0 0 * 4.16667 0 0 4.58333 0 0 * 5 0.5 50 5.41667 1 0 * 5.83333 1 0 6.25 1 0 * 6.66667 1 0 7.08333 1 0 * 7.5 1 0 7.91667 1 0 * 8.33333 1 0 8.75 1 0 * 9.16667 1 0 9.58333 1 0 * 10 1 0 Problem 5 DeBoor's Titanium property data X Y Y' * 595 0.644 -0.0022 600 0.633 -0.0022 * 605 0.622 0.0016 610 0.63 0.0016 * 615 0.638 0.0011 620 0.6435 0.0011 * 625 0.649 0.0003 630 0.6505 0.0003 * 635 0.652 -0.0013 640 0.6455 -0.0013 * 645 0.639 0.0007 650 0.6425 0.0007 * 655 0.646 0.0011 660 0.6515 0.0011 * 665 0.657 -0.0005 670 0.6545 -0.0005 * 675 0.652 0.0003 680 0.6535 0.0003 * 685 0.655 -0.0011 690 0.6495 -0.0011 * 695 0.644 0.0019 700 0.6535 0.0019 * 705 0.663 0 710 0.663 0 * 715 0.663 0.0005 720 0.6655 0.0005 * 725 0.668 0.0008 730 0.672 0.0008 * 735 0.676 0 740 0.676 0 * 745 0.676 0.001 750 0.681 0.001 * 755 0.686 -0.0007 760 0.6825 -0.0007 * 765 0.679 -0.0001 770 0.6785 -0.0001 * 775 0.678 0.0005 780 0.6805 0.0005 * 785 0.683 0.0011 790 0.6885 0.0011 * 795 0.694 0.0005 800 0.6965 0.0005 * 805 0.699 0.0011 810 0.7045 0.0011 * 815 0.71 0.002 820 0.72 0.002 * 825 0.73 0.0033 830 0.7465 0.0033 * 835 0.763 0.0049 840 0.7875 0.0049 * 845 0.812 0.0095 850 0.8595 0.0095 * 855 0.907 0.0137 860 0.9755 0.0137 * 865 1.044 0.0292 870 1.19 0.0292 * 875 1.336 0.0545 880 1.6085 0.0545 * 885 1.881 0.0288 890 2.025 0.0288 * 895 2.169 -0.0094 900 2.122 -0.0094 * 905 2.075 -0.0477 910 1.8365 -0.0477 * 915 1.598 -0.0387 920 1.4045 -0.0387 * 925 1.211 -0.0295 930 1.0635 -0.0295 * 935 0.916 -0.017 940 0.831 -0.017 * 945 0.746 -0.0074 950 0.709 -0.0074 * 955 0.672 -0.0045 960 0.6495 -0.0045 * 965 0.627 -0.0012 970 0.621 -0.0012 * 975 0.615 -0.0008 980 0.611 -0.0008 * 985 0.607 -0.0001 990 0.6065 -0.0001 * 995 0.606 0.0003 1000 0.6075 0.0003 * 1005 0.609 -0.0006 1010 0.606 -0.0006 * 1015 0.603 -0.0002 1020 0.602 -0.0002 * 1025 0.601 0.0002 1030 0.602 0.0002 * 1035 0.603 -0.0002 1040 0.602 -0.0002 * 1045 0.601 0.001 1050 0.606 0.001 * 1055 0.611 -0.001 1060 0.606 -0.001 * 1065 0.601 0.0007 1070 0.6045 0.0007 * 1075 0.608 0.0007 Problem 6 The Sawtooth data X Y Y' * 0 0 2 0.0833333 0.166667 2 * 0.166667 0.333333 2 0.25 0.5 2 * 0.333333 0.666667 2 0.416667 0.833333 2 * 0.5 1 -2 0.583333 0.833333 -2 * 0.666667 0.666667 -2 0.75 0.5 -2 * 0.833333 0.333333 -2 0.916667 0.166667 -2 * 1 0 2 1.08333 0.166667 2 * 1.16667 0.333333 2 1.25 0.5 2 * 1.33333 0.666667 2 1.41667 0.833333 2 * 1.5 1 -2 1.58333 0.833333 -2 * 1.66667 0.666667 -2 1.75 0.5 -2 * 1.83333 0.333333 -2 1.91667 0.166667 -2 * 2 0 2 2.08333 0.166667 2 * 2.16667 0.333333 2 2.25 0.5 2 * 2.33333 0.666667 2 2.41667 0.833333 2 * 2.5 1 -2 2.58333 0.833333 -2 * 2.66667 0.666667 -2 2.75 0.5 -2 * 2.83333 0.333333 -2 2.91667 0.166667 -2 * 3 0 2 3.08333 0.166667 2 * 3.16667 0.333333 2 3.25 0.5 2 * 3.33333 0.666667 2 3.41667 0.833333 2 * 3.5 1 -2 3.58333 0.833333 -2 * 3.66667 0.666667 -2 3.75 0.5 -2 * 3.83333 0.333333 -2 3.91667 0.166667 -2 * 4 0 2 4.08333 0.166667 2 * 4.16667 0.333333 2 4.25 0.5 2 * 4.33333 0.666667 2 4.41667 0.833333 2 * 4.5 1 -2 4.58333 0.833333 -2 * 4.66667 0.666667 -2 4.75 0.5 -2 * 4.83333 0.333333 -2 4.91667 0.166667 -2 * 5 0 -2 Problem 7 Concavity test data X Y Y' * 0 0 9 0.0625 0.5625 9 * 0.125 0.9125 0.5 0.1875 0.94375 0.5 * 0.25 0.925 -0.5 0.3125 0.8 -8 * 0.375 0.3 -8 0.4375 0.08125 -0.5 * 0.5 0.05 0 0.5625 0.05 0 * 0.625 0.06875 0.75 0.6875 0.115625 0.75 * 0.75 0.1625 0.75 0.8125 0.25 4 * 0.875 0.5 4 0.9375 0.75 4 * 1 1 4 Problem 8 Extrapolation test data X Y Y' * 0 0 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 5.9084 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 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 0.57064 * 173.091 62.2454 0.57064 183.909 69.6033 0.977851 * 194.727 80.1158 0.939623 205.545 90.4217 1.19777 * 216.364 103.346 1.17364 227.182 117.17 1.69032 * 238 135.457 1.69032 Problem 9 Sunspot data, 1700-1960. X Y Y' * 1700 5 6 1700.5 8 6 * 1701 11 5 1701.5 13.5 5 * 1702 16 7 1702.5 19.5 7 * 1703 23 13 1703.5 29.5 13 * 1704 36 22 1704.5 47 22 * 1705 58 -29 1705.5 43.5 -29 * 1706 29 -9 1706.5 24.5 -9 * 1707 20 -10 1707.5 15 -10 * 1708 10 -2 1708.5 9 -2 * 1709 8 -5 1709.5 5.5 -5 * 1710 3 -3 1710.5 1.5 -3 * 1711 0 0 1711.5 0 0 * 1712 0 2 1712.5 1 2 * 1713 2 9 1713.5 6.5 9 * 1714 11 16 1714.5 19 16 * 1715 27 20 1715.5 37 20 * 1716 47 16 1716.5 55 16 * 1717 63 -3 1717.5 61.5 -3 * 1718 60 -21 1718.5 49.5 -21 * 1719 39 -11 1719.5 33.5 -11 * 1720 28 -2 1720.5 27 -2 * 1721 26 -4 1721.5 24 -4 * 1722 22 -11 1722.5 16.5 -11 * 1723 11 10 1723.5 16 10 * 1724 21 19 1724.5 30.5 19 * 1725 40 38 1725.5 59 38 * 1726 78 44 1726.5 100 44 * 1727 122 -19 1727.5 112.5 -19 * 1728 103 -30 1728.5 88 -30 * 1729 73 -26 1729.5 60 -26 * 1730 47 -12 1730.5 41 -12 * 1731 35 -24 1731.5 23 -24 * 1732 11 -6 1732.5 8 -6 * 1733 5 11 1733.5 10.5 11 * 1734 16 18 1734.5 25 18 * 1735 34 36 1735.5 52 36 * 1736 70 11 1736.5 75.5 11 * 1737 81 30 1737.5 96 30 * 1738 111 -10 1738.5 106 -10 * 1739 101 -28 1739.5 87 -28 * 1740 73 -33 1740.5 56.5 -33 * 1741 40 -20 1741.5 30 -20 * 1742 20 -4 1742.5 18 -4 * 1743 16 -11 1743.5 10.5 -11 * 1744 5 6 1744.5 8 6 * 1745 11 11 1745.5 16.5 11 * 1746 22 18 1746.5 31 18 * 1747 40 20 1747.5 50 20 * 1748 60 20.9 1748.5 70.45 20.9 * 1749 80.9 2.5 1749.5 82.15 2.5 * 1750 83.4 -35.7 1750.5 65.55 -35.7 * 1751 47.7 0.1 1751.5 47.75 0.1 * 1752 47.8 -17.1 1752.5 39.25 -17.1 * 1753 30.7 -18.5 1753.5 21.45 -18.5 * 1754 12.2 -2.6 1754.5 10.9 -2.6 * 1755 9.6 0.6 1755.5 9.9 0.6 * 1756 10.2 22.2 1756.5 21.3 22.2 * 1757 32.4 15.2 1757.5 40 15.2 * 1758 47.6 6.4 1758.5 50.8 6.4 * 1759 54 8.9 1759.5 58.45 8.9 * 1760 62.9 23 1760.5 74.4 23 * 1761 85.9 -24.7 1761.5 73.55 -24.7 * 1762 61.2 -16.1 1762.5 53.15 -16.1 * 1763 45.1 -8.7 1763.5 40.75 -8.7 * 1764 36.4 -15.5 1764.5 28.65 -15.5 * 1765 20.9 -9.5 1765.5 16.15 -9.5 * 1766 11.4 26.4 1766.5 24.6 26.4 * 1767 37.8 32 1767.5 53.8 32 * 1768 69.8 36.3 1768.5 87.95 36.3 * 1769 106.1 -5.3 1769.5 103.45 -5.3 * 1770 100.8 -19.2 1770.5 91.2 -19.2 * 1771 81.6 -15.1 1771.5 74.05 -15.1 * 1772 66.5 -31.7 1772.5 50.65 -31.7 * 1773 34.8 -4.2 1773.5 32.7 -4.2 * 1774 30.6 -23.6 1774.5 18.8 -23.6 * 1775 7 12.8 1775.5 13.4 12.8 * 1776 19.8 72.7 1776.5 56.15 72.7 * 1777 92.5 61.9 1777.5 123.45 61.9 * 1778 154.4 -28.5 1778.5 140.15 -28.5 * 1779 125.9 -41.1 1779.5 105.35 -41.1 * 1780 84.8 -16.7 1780.5 76.45 -16.7 * 1781 68.1 -29.6 1781.5 53.3 -29.6 * 1782 38.5 -15.7 1782.5 30.65 -15.7 * 1783 22.8 -12.6 1783.5 16.5 -12.6 * 1784 10.2 13.9 1784.5 17.15 13.9 * 1785 24.1 58.8 1785.5 53.5 58.8 * 1786 82.9 49.1 1786.5 107.45 49.1 * 1787 132 -1.1 1787.5 131.45 -1.1 * 1788 130.9 -12.8 1788.5 124.5 -12.8 * 1789 118.1 -28.2 1789.5 104 -28.2 * 1790 89.9 -23.3 1790.5 78.25 -23.3 * 1791 66.6 -6.6 1791.5 63.3 -6.6 * 1792 60 -13.1 1792.5 53.45 -13.1 * 1793 46.9 -5.9 1793.5 43.95 -5.9 * 1794 41 -19.7 1794.5 31.15 -19.7 * 1795 21.3 -5.3 1795.5 18.65 -5.3 * 1796 16 -9.6 1796.5 11.2 -9.6 * 1797 6.4 -2.3 1797.5 5.25 -2.3 * 1798 4.1 2.7 1798.5 5.45 2.7 * 1799 6.8 7.7 1799.5 10.65 7.7 * 1800 14.5 19.5 1800.5 24.25 19.5 * 1801 34 11 1801.5 39.5 11 * 1802 45 -1.9 1802.5 44.05 -1.9 * 1803 43.1 4.4 1803.5 45.3 4.4 * 1804 47.5 -5.3 1804.5 44.85 -5.3 * 1805 42.2 -14.1 1805.5 35.15 -14.1 * 1806 28.1 -18 1806.5 19.1 -18 * 1807 10.1 -2 1807.5 9.1 -2 * 1808 8.1 -5.6 1808.5 5.3 -5.6 * 1809 2.5 -2.5 1809.5 1.25 -2.5 * 1810 0 1.4 1810.5 0.7 1.4 * 1811 1.4 3.6 1811.5 3.2 3.6 * 1812 5 7.2 1812.5 8.6 7.2 * 1813 12.2 1.7 1813.5 13.05 1.7 * 1814 13.9 21.5 1814.5 24.65 21.5 * 1815 35.4 10.4 1815.5 40.6 10.4 * 1816 45.8 -4.7 1816.5 43.45 -4.7 * 1817 41.1 -11 1817.5 35.6 -11 * 1818 30.1 -6.2 1818.5 27 -6.2 * 1819 23.9 -8.3 1819.5 19.75 -8.3 * 1820 15.6 -9 1820.5 11.1 -9 * 1821 6.6 -2.6 1821.5 5.3 -2.6 * 1822 4 -2.2 1822.5 2.9 -2.2 * 1823 1.8 6.7 1823.5 5.15 6.7 * 1824 8.5 8.1 1824.5 12.55 8.1 * 1825 16.6 19.7 1825.5 26.45 19.7 * 1826 36.3 13.3 1826.5 42.95 13.3 * 1827 49.6 14.6 1827.5 56.9 14.6 * 1828 64.2 2.8 1828.5 65.6 2.8 * 1829 67 3.9 1829.5 68.95 3.9 * 1830 70.9 -23.1 1830.5 59.35 -23.1 * 1831 47.8 -20.3 1831.5 37.65 -20.3 * 1832 27.5 -19 1832.5 18 -19 * 1833 8.5 4.7 1833.5 10.85 4.7 * 1834 13.2 43.7 1834.5 35.05 43.7 * 1835 56.9 64.6 1835.5 89.2 64.6 * 1836 121.5 16.8 1836.5 129.9 16.8 * 1837 138.3 -35.1 1837.5 120.75 -35.1 * 1838 103.2 -17.5 1838.5 94.45 -17.5 * 1839 85.7 -21.1 1839.5 75.15 -21.1 * 1840 64.6 -27.9 1840.5 50.65 -27.9 * 1841 36.7 -12.5 1841.5 30.45 -12.5 * 1842 24.2 -13.5 1842.5 17.45 -13.5 * 1843 10.7 4.3 1843.5 12.85 4.3 * 1844 15 25.1 1844.5 27.55 25.1 * 1845 40.1 21.4 1845.5 50.8 21.4 * 1846 61.5 37 1846.5 80 37 * 1847 98.5 26.2 1847.5 111.6 26.2 * 1848 124.7 -28.4 1848.5 110.5 -28.4 * 1849 96.3 -29.7 1849.5 81.45 -29.7 * 1850 66.6 -2.1 1850.5 65.55 -2.1 * 1851 64.5 -10.4 1851.5 59.3 -10.4 * 1852 54.1 -15.1 1852.5 46.55 -15.1 * 1853 39 -18.4 1853.5 29.8 -18.4 * 1854 20.6 -13.9 1854.5 13.65 -13.9 * 1855 6.7 -2.4 1855.5 5.5 -2.4 * 1856 4.3 18.4 1856.5 13.5 18.4 * 1857 22.7 32.1 1857.5 38.75 32.1 * 1858 54.8 39 1858.5 74.3 39 * 1859 93.8 2 1859.5 94.8 2 * 1860 95.8 -18.6 1860.5 86.5 -18.6 * 1861 77.2 -18.1 1861.5 68.15 -18.1 * 1862 59.1 -15.1 1862.5 51.55 -15.1 * 1863 44 3 1863.5 45.5 3 * 1864 47 -16.5 1864.5 38.75 -16.5 * 1865 30.5 -14.2 1865.5 23.4 -14.2 * 1866 16.3 -9 1866.5 11.8 -9 * 1867 7.3 30.3 1867.5 22.45 30.3 * 1868 37.6 36.4 1868.5 55.8 36.4 * 1869 74 65 1869.5 106.5 65 * 1870 139 -27.8 1870.5 125.1 -27.8 * 1871 111.2 -9.6 1871.5 106.4 -9.6 * 1872 101.6 -35.4 1872.5 83.9 -35.4 * 1873 66.2 -21.5 1873.5 55.45 -21.5 * 1874 44.7 -27.7 1874.5 30.85 -27.7 * 1875 17 -5.7 1875.5 14.15 -5.7 * 1876 11.3 1.1 1876.5 11.85 1.1 * 1877 12.4 -9 1877.5 7.9 -9 * 1878 3.4 2.6 1878.5 4.7 2.6 * 1879 6 26.3 1879.5 19.15 26.3 * 1880 32.3 22 1880.5 43.3 22 * 1881 54.3 5.4 1881.5 57 5.4 * 1882 59.7 4 1882.5 61.7 4 * 1883 63.7 -0.2 1883.5 63.6 -0.2 * 1884 63.5 -11.3 1884.5 57.85 -11.3 * 1885 52.2 -26.8 1885.5 38.8 -26.8 * 1886 25.4 -12.3 1886.5 19.25 -12.3 * 1887 13.1 -6.3 1887.5 9.95 -6.3 * 1888 6.8 -0.5 1888.5 6.55 -0.5 * 1889 6.3 0.8 1889.5 6.7 0.8 * 1890 7.1 28.5 1890.5 21.35 28.5 * 1891 35.6 37.4 1891.5 54.3 37.4 * 1892 73 12.1 1892.5 79.05 12.1 * 1893 85.1 -7.1 1893.5 81.55 -7.1 * 1894 78 -14 1894.5 71 -14 * 1895 64 -22.2 1895.5 52.9 -22.2 * 1896 41.8 -15.6 1896.5 34 -15.6 * 1897 26.2 0.5 1897.5 26.45 0.5 * 1898 26.7 -14.6 1898.5 19.4 -14.6 * 1899 12.1 -2.6 1899.5 10.8 -2.6 * 1900 9.5 -6.8 1900.5 6.1 -6.8 * 1901 2.7 2.3 1901.5 3.85 2.3 * 1902 5 19.4 1902.5 14.7 19.4 * 1903 24.4 17.6 1903.5 33.2 17.6 * 1904 42 21.5 1904.5 52.75 21.5 * 1905 63.5 -9.7 1905.5 58.65 -9.7 * 1906 53.8 8.2 1906.5 57.9 8.2 * 1907 62 -13.5 1907.5 55.25 -13.5 * 1908 48.5 -4.6 1908.5 46.2 -4.6 * 1909 43.9 -25.3 1909.5 31.25 -25.3 * 1910 18.6 -12.9 1910.5 12.15 -12.9 * 1911 5.7 -2.1 1911.5 4.65 -2.1 * 1912 3.6 -2.2 1912.5 2.5 -2.2 * 1913 1.4 8.2 1913.5 5.5 8.2 * 1914 9.6 37.8 1914.5 28.5 37.8 * 1915 47.4 9.7 1915.5 52.25 9.7 * 1916 57.1 46.8 1916.5 80.5 46.8 * 1917 103.9 -23.3 1917.5 92.25 -23.3 * 1918 80.6 -17 1918.5 72.1 -17 * 1919 63.6 -26 1919.5 50.6 -26 * 1920 37.6 -11.5 1920.5 31.85 -11.5 * 1921 26.1 -11.9 1921.5 20.15 -11.9 * 1922 14.2 -8.4 1922.5 10 -8.4 * 1923 5.8 10.9 1923.5 11.25 10.9 * 1924 16.7 27.6 1924.5 30.5 27.6 * 1925 44.3 19.6 1925.5 54.1 19.6 * 1926 63.9 5.1 1926.5 66.45 5.1 * 1927 69 8.8 1927.5 73.4 8.8 * 1928 77.8 -12.9 1928.5 71.35 -12.9 * 1929 64.9 -29.2 1929.5 50.3 -29.2 * 1930 35.7 -14.5 1930.5 28.45 -14.5 * 1931 21.2 -10.1 1931.5 16.15 -10.1 * 1932 11.1 -5.4 1932.5 8.4 -5.4 * 1933 5.7 3 1933.5 7.2 3 * 1934 8.7 27.4 1934.5 22.4 27.4 * 1935 36.1 43.6 1935.5 57.9 43.6 * 1936 79.7 34.7 1936.5 97.05 34.7 * 1937 114.4 -4.8 1937.5 112 -4.8 * 1938 109.6 -20.8 1938.5 99.2 -20.8 * 1939 88.8 -21 1939.5 78.3 -21 * 1940 67.8 -20.3 1940.5 57.65 -20.3 * 1941 47.5 -16.9 1941.5 39.05 -16.9 * 1942 30.6 -14.3 1942.5 23.45 -14.3 * 1943 16.3 -6.7 1943.5 12.95 -6.7 * 1944 9.6 23.6 1944.5 21.4 23.6 * 1945 33.2 59.4 1945.5 62.9 59.4 * 1946 92.6 59 1946.5 122.1 59 * 1947 151.6 -15.3 1947.5 143.95 -15.3 * 1948 136.3 -1.6 1948.5 135.5 -1.6 * 1949 134.7 -50.8 1949.5 109.3 -50.8 * 1950 83.9 -14.5 1950.5 76.65 -14.5 * 1951 69.4 -37.9 1951.5 50.45 -37.9 * 1952 31.5 -17.6 1952.5 22.7 -17.6 * 1953 13.9 -9.5 1953.5 9.15 -9.5 * 1954 4.4 33.6 1954.5 21.2 33.6 * 1955 38 103.7 1955.5 89.85 103.7 * 1956 141.7 48.5 1956.5 165.95 48.5 * 1957 190.2 -5.4 1957.5 187.5 -5.4 * 1958 184.8 -25.8 1958.5 171.9 -25.8 * 1959 159 -46.7 1959.5 135.65 -46.7 * 1960 112.3 -46.7 Problem 10 Y = 2 + 5*X + 10*N(0,1). X Y Y' * -1.9935 -1.8918 -64.019 -1.95873 -4.11792 -64.019 * -1.92395 -6.34403 -64.019 -1.88918 -8.57015 -64.019 * -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 -1.611 -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 * -1.2285 -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 3.1097 -41.5435 -0.985091 1.97352 46.3426 * -0.950318 3.58498 46.3426 -0.915545 5.19644 46.3426 * -0.880773 6.8079 46.3426 -0.846 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 1.1555 -106.897 -0.637364 -2.56161 -106.897 * -0.602591 -6.3868 -112.066 -0.567818 -6.06394 10.3087 * -0.533045 -5.70547 10.3087 -0.498273 -5.34701 10.3087 * -0.4635 -4.98855 10.3087 -0.428727 -4.63009 10.3087 * -0.393955 -4.27163 10.3087 -0.359182 -3.91316 10.3087 * -0.324409 -3.5547 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 -0.081 -5.9836 115.342 * -0.0462273 -2.9362 25.9176 -0.0114545 -2.03497 25.9176 * 0.0233182 -1.13374 25.9176 0.0580909 -0.232518 25.9176 * 0.0928636 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 * 0.3015 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 6.7409 -848.922 * 0.510136 -0.176991 111.356 0.544909 3.69515 111.356 * 0.579682 7.5673 111.356 0.614455 9.269 -98.2559 * 0.649227 5.85238 -98.2559 0.684 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 -1.6331 -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 * 1.0665 -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 19.913 -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 1.449 8.44777 -73.9486 * 1.48377 5.87638 -73.9486 1.51855 3.30498 -73.9486 * 1.55332 0.733589 -73.9486 1.58809 3.7397 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 4.2888 -72.0872 1.79673 13.6725 472.662 * 1.8315 25.4827 -98.3919 1.86627 22.0614 -98.3919 * 1.90105 18.64 -98.3919 1.93582 15.2187 -98.3919 * 1.97059 11.7973 -98.3919 2.00536 9.312 490.416 * 2.04014 -8.008 297.09 2.07491 2.32263 297.09 * 2.10968 17.1897 -49.3888 2.14445 15.4723 -49.3888 * 2.17923 13.7549 -49.3888 2.214 10.8975 -177.484 * 2.24877 4.7259 -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 -87.166 * 2.45741 20.3587 -87.166 2.49218 17.3277 -87.166 * 2.52695 14.2967 -87.166 2.56173 11.2657 -87.166 * 2.5965 11.5279 802.902 2.63127 32.047 -149.147 * 2.66605 26.8608 -149.147 2.70082 21.6745 -149.147 * 2.73559 16.4882 -149.147 2.77036 11.302 -149.147 * 2.80514 6.11573 -149.147 2.83991 10.1037 167.108 * 2.87468 15.9145 167.108 2.90945 13.4396 -254.46 * 2.94423 4.59133 -254.46 2.979 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 -32.565 * 3.29195 19.4118 -32.565 3.32673 18.2794 -32.565 * 3.3615 17.147 -32.565 3.39627 16.0147 -32.565 * 3.43105 16.2987 65.486 3.46582 18.5758 65.486 * 3.50059 20.8529 65.486 3.53536 23.1301 65.486 * 3.57014 25.4072 65.486 3.60491 27.6843 65.486 * 3.63968 28.266 1.70238 3.67445 21.9916 60.2056 * 3.70923 24.0851 60.2056 3.744 26.1787 60.2056 * 3.77877 14.156 -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 * 4.1265 30.561 91.9827 4.16127 32.5031 -133.465 * 4.19605 27.8622 -133.465 4.23082 23.2213 -133.465 * 4.26559 25.8217 -80.238 4.30036 23.0316 -80.238 * 4.33514 24.5915 272.371 4.36991 26.972 32.8992 * 4.40468 28.116 32.8992 4.43945 25.6122 -120.663 * 4.47423 21.4164 -120.663 4.509 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 38.114 -325.755 * 4.82195 26.7866 -325.755 4.85673 19.8232 -21.1629 * 4.8915 19.0873 -21.1629 TEST05 Overhauser spline interpolation. Problem 1 DeBoor example, Mars position X Y * 1250.5 1.3914 1255.5 1.38602 * 1260.5 1.37696 1265.5 1.3642 * 1270.5 1.34783 1275.5 1.32792 * 1280.5 1.30456 1285.5 1.27784 * 1290.5 1.24787 1295.5 1.21476 * 1300.5 1.17862 1305.5 1.13957 * 1310.5 1.09776 1315.5 1.05331 * 1320.5 1.00636 1325.5 0.957052 * 1330.5 0.90553 1335.5 0.85201 * 1340.5 0.79642 Problem 2 DeBoor example, roughly linear data X Y * 1 0 1.5 0.22875 * 2 0.6 2.5 1.21313 * 3 1.77 3.5 1.83125 * 4 1.92 4.5 2.61125 * 5 3.31 5.5 3.435 * 6 3.52 6.5 4.02313 * 7 4.59 7.5 4.98687 * 8 5.31 8.5 5.51562 * 9 5.79 9.5 6.44812 * 10 7.06 10.5 7.26 * 11 7.17 Problem 3 The pulse data, 0 0 0 0 0 1 0 0 0 0 0 X Y * 0 0 0.5 0 * 1 0 1.5 0 * 2 0 2.5 0 * 3 0 3.5 -0.0625 * 4 0 4.5 0.5625 * 5 1 5.5 0.5625 * 6 0 6.5 -0.0625 * 7 0 7.5 0 * 8 0 8.5 0 * 9 0 9.5 0 * 10 0 Problem 4 The jump data, 0 0 0 0 0 1/2 1 1 1 1 1 X Y * 0 0 0.5 0 * 1 0 1.5 0 * 2 0 2.5 0 * 3 0 3.5 0 * 4 0 4.495 -6.12563 * 4.99 0 4.995 0.249375 * 5 0.5 5.005 0.750625 * 5.01 1 5.505 7.12563 * 6 1 6.5 1 * 7 1 7.5 1 * 8 1 8.5 1 * 9 1 9.5 1 * 10 1 Problem 5 DeBoor's Titanium property data X Y * 595 0.644 600 0.62825 * 605 0.622 610 0.627938 * 615 0.638 620 0.644313 * 625 0.649 630 0.652 * 635 0.652 640 0.64525 * 645 0.639 650 0.641 * 655 0.646 660 0.65225 * 665 0.657 670 0.655 * 675 0.652 680 0.653875 * 685 0.655 690 0.6485 * 695 0.644 700 0.652813 * 705 0.663 710 0.663875 * 715 0.663 720 0.665 * 725 0.668 730 0.672313 * 735 0.676 740 0.675875 * 745 0.676 750 0.681438 * 755 0.686 760 0.683188 * 765 0.679 770 0.67775 * 775 0.678 780 0.67975 * 785 0.683 790 0.6885 * 795 0.694 800 0.6965 * 805 0.699 810 0.703562 * 815 0.71 820 0.718625 * 825 0.73 830 0.744687 * 835 0.763 840 0.783625 * 845 0.812 850 0.854 * 855 0.907 860 0.963188 * 865 1.044 870 1.1645 * 875 1.336 880 1.60875 * 885 1.881 890 2.06494 * 895 2.169 900 2.16981 * 905 2.075 910 1.85481 * 915 1.598 920 1.39313 * 925 1.211 930 1.04994 * 935 0.916 940 0.817187 * 945 0.746 950 0.701188 * 955 0.672 960 0.645625 * 965 0.627 970 0.618687 * 975 0.615 980 0.610313 * 985 0.607 990 0.605812 * 995 0.606 1000 0.607812 * 1005 0.609 1010 0.606313 * 1015 0.603 1020 0.6015 * 1025 0.601 1030 0.602 * 1035 0.603 1040 0.6015 * 1045 0.601 1050 0.6065 * 1055 0.611 1060 0.606188 * 1065 0.601 1070 0.602375 * 1075 0.608 Problem 6 The Sawtooth data X Y * 0 0 0.25 0.75 * 0.5 1 0.75 0.458333 * 1 0 1.125 0.208333 * 1.25 0.5 1.375 0.8125 * 1.5 1 1.625 0.8125 * 1.75 0.5 1.875 0.175 * 2 0 2.08333 0.133333 * 2.16667 0.333333 2.25 0.5 * 2.33333 0.666667 2.41667 0.875 * 2.5 1 2.58333 0.875 * 2.66667 0.666667 2.75 0.5 * 2.83333 0.333333 2.91667 0.119048 * 3 -5.55112e-17 3.0625 0.0982143 * 3.125 0.25 3.1875 0.375 * 3.25 0.5 3.3125 0.625 * 3.375 0.75 3.4375 0.90625 * 3.5 1 3.5625 0.90625 * 3.625 0.75 3.6875 0.625 * 3.75 0.5 3.8125 0.375 * 3.875 0.25 3.9375 0.0902778 * 4 0 4.05 0.0777778 * 4.1 0.2 4.15 0.3 * 4.2 0.4 4.25 0.5 * 4.3 0.6 4.35 0.7 * 4.4 0.8 4.45 0.925 * 4.5 1 4.55 0.925 * 4.6 0.8 4.65 0.7 * 4.7 0.6 4.75 0.5 * 4.8 0.4 4.85 0.3 * 4.9 0.2 4.95 0.1 * 5 0 Problem 7 Concavity test data X Y * 0 0 0.05 0.55625 * 0.1 0.9 0.15 0.984375 * 0.2 0.95 0.25 0.978125 * 0.3 0.9 0.35 0.5 * 0.4 0.1 0.45 0.025 * 0.5 0.05 0.55 0.04375 * 0.6 0.05 0.7 0.071875 * 0.8 0.2 0.9 0.51875 * 1 1 Problem 8 Extrapolation test data X Y * 0 0 35.5 0.812936 * 71 7.7554 87.5 13.0838 * 104 19.7062 119.5 26.678 * 135 35.5379 140 39.1309 * 145 42.9154 152.5 48.9577 * 160 54.7752 170.5 60.4236 * 181 66.7587 187 72.4323 * 193 78.4929 199 83.9481 * 205 89.7683 210 95.6256 * 215 101.746 220 107.348 * 225 113.482 231.5 123.52 * 238 135.457 Problem 9 Sunspot data, 1700-1960. X Y * 1700 5 1700.5 8.125 * 1701 11 1701.5 13.4375 * 1702 16 1702.5 19 * 1703 23 1703.5 28.5625 * 1704 36 1704.5 49.625 * 1705 58 1705.5 45.4375 * 1706 29 1706.5 23.3125 * 1707 20 1707.5 14.5625 * 1708 10 1708.5 8.6875 * 1709 8 1709.5 5.5625 * 1710 3 1710.5 1.1875 * 1711 0 1711.5 -0.3125 * 1712 0 1712.5 0.4375 * 1713 2 1713.5 5.625 * 1714 11 1714.5 18.3125 * 1715 27 1715.5 37 * 1716 47 1716.5 56.4375 * 1717 63 1717.5 63.8125 * 1718 60 1718.5 50 * 1719 39 1719.5 32.3125 * 1720 28 1720.5 26.5625 * 1721 26 1721.5 24.5625 * 1722 22 1722.5 15.625 * 1723 11 1723.5 14.125 * 1724 21 1724.5 28.75 * 1725 40 1725.5 57.4375 * 1726 78 1726.5 103.562 * 1727 122 1727.5 117.125 * 1728 103 1728.5 88.4375 * 1729 73 1729.5 58.875 * 1730 47 1730.5 40.875 * 1731 35 1731.5 22.625 * 1732 11 1732.5 5.8125 * 1733 5 1733.5 9 * 1734 16 1734.5 23.4375 * 1735 34 1735.5 52.4375 * 1736 70 1736.5 75.875 * 1737 81 1737.5 97.3125 * 1738 111 1738.5 109.625 * 1739 101 1739.5 88.4375 * 1740 73 1740.5 56 * 1741 40 1741.5 28.1875 * 1742 20 1742.5 17.4375 * 1743 16 1743.5 9.875 * 1744 5 1744.5 6.625 * 1745 11 1745.5 15.75 * 1746 22 1746.5 30.4375 * 1747 40 1747.5 49.8188 * 1748 60 1748.5 71.5438 * 1749 80.9 1749.5 85.6875 * 1750 83.4 1750.5 65.7 * 1751 47.7 1751.5 46.5875 * 1752 47.8 1752.5 40.4125 * 1753 30.7 1753.5 20.5438 * 1754 12.2 1754.5 9.70625 * 1755 9.6 1755.5 8.35 * 1756 10.2 1756.5 20.3875 * 1757 32.4 1757.5 40.9875 * 1758 47.6 1758.5 51.1938 * 1759 54 1759.5 57.4125 * 1760 62.9 1760.5 76.5 * 1761 85.9 1761.5 75.9938 * 1762 61.2 1762.5 52.15 * 1763 45.1 1763.5 40.7125 * 1764 36.4 1764.5 28.7 * 1765 20.9 1765.5 13.5312 * 1766 11.4 1766.5 22.0062 * 1767 37.8 1767.5 53.1812 * 1768 69.8 1768.5 90.2812 * 1769 106.1 1769.5 106.919 * 1770 100.8 1770.5 91.8125 * 1771 81.6 1771.5 74.8312 * 1772 66.5 1772.5 49.9688 * 1773 34.8 1773.5 32.1937 * 1774 30.6 1774.5 17.7375 * 1775 7 1775.5 7.38125 * 1776 19.8 1776.5 53.0812 * 1777 92.5 1777.5 129.775 * 1778 154.4 1778.5 146.587 * 1779 125.9 1779.5 104.613 * 1780 84.8 1780.5 75.7312 * 1781 68.1 1781.5 53.2375 * 1782 38.5 1782.5 29.5875 * 1783 22.8 1783.5 14.65 * 1784 10.2 1784.5 12.6875 * 1785 24.1 1785.5 51.3 * 1786 82.9 1786.5 111.194 * 1787 132 1787.5 135.319 * 1788 130.9 1788.5 126.194 * 1789 118.1 1789.5 104.656 * 1790 89.9 1790.5 76.9 * 1791 66.6 1791.5 62.6625 * 1792 60 1792.5 53.4062 * 1793 46.9 1793.5 44.3625 * 1794 41 1794.5 31.1125 * 1795 21.3 1795.5 18.0187 * 1796 16 1796.5 11.0125 * 1797 6.4 1797.5 4.48125 * 1798 4.1 1798.5 4.825 * 1799 6.8 1799.5 9.6 * 1800 14.5 1800.5 24.0438 * 1801 34 1801.5 40.8375 * 1802 45 1802.5 44.4625 * 1803 43.1 1803.5 45.5125 * 1804 47.5 1804.5 46.0063 * 1805 42.2 1805.5 35.9438 * 1806 28.1 1806.5 18.3438 * 1807 10.1 1807.5 8.325 * 1808 8.1 1808.5 5.33125 * 1809 2.5 1809.5 0.8125 * 1810 0 1810.5 0.31875 * 1811 1.4 1811.5 2.8375 * 1812 5 1812.5 8.71875 * 1813 12.2 1813.5 12.1562 * 1814 13.9 1814.5 24.1063 * 1815 35.4 1815.5 42.2375 * 1816 45.8 1816.5 44.7875 * 1817 41.1 1817.5 35.6938 * 1818 30.1 1818.5 26.8312 * 1819 23.9 1819.5 19.925 * 1820 15.6 1820.5 10.7438 * 1821 6.6 1821.5 4.875 * 1822 4 1822.5 2.31875 * 1823 1.8 1823.5 4.50625 * 1824 8.5 1824.5 11.7375 * 1825 16.6 1825.5 26.125 * 1826 36.3 1826.5 43.2687 * 1827 49.6 1827.5 57.5563 * 1828 64.2 1828.5 66.2688 * 1829 67 1829.5 70.5687 * 1830 70.9 1830.5 60.8625 * 1831 47.8 1831.5 37.3937 * 1832 27.5 1832.5 16.4375 * 1833 8.5 1833.5 6.93125 * 1834 13.2 1834.5 31.3062 * 1835 56.9 1835.5 90.8812 * 1836 121.5 1836.5 136.131 * 1837 138.3 1837.5 122.894 * 1838 103.2 1838.5 93.575 * 1839 85.7 1839.5 75.8 * 1840 64.6 1840.5 50.1125 * 1841 36.7 1841.5 29.55 * 1842 24.2 1842.5 16.4 * 1843 10.7 1843.5 10.4375 * 1844 15 1844.5 26.4813 * 1845 40.1 1845.5 50.0563 * 1846 61.5 1846.5 79.7 * 1847 98.5 1847.5 115.688 * 1848 124.7 1848.5 113.994 * 1849 96.3 1849.5 79.8063 * 1850 66.6 1850.5 64.3438 * 1851 64.5 1851.5 60.1125 * 1852 54.1 1852.5 47.05 * 1853 39 1853.5 29.725 * 1854 20.6 1854.5 12.65 * 1855 6.7 1855.5 3.48125 * 1856 4.3 1856.5 11.3437 * 1857 22.7 1857.5 37.4625 * 1858 54.8 1858.5 76.1813 * 1859 93.8 1859.5 98.4 * 1860 95.8 1860.5 87.7562 * 1861 77.2 1861.5 67.9313 * 1862 59.1 1862.5 50.2313 * 1863 44 1863.5 45.5875 * 1864 47 1864.5 39.825 * 1865 30.5 1865.5 22.9312 * 1866 16.3 1866.5 9.01875 * 1867 7.3 1867.5 19.6125 * 1868 37.6 1868.5 53.6313 * 1869 74 1869.5 110.512 * 1870 139 1870.5 129.762 * 1871 111.2 1871.5 106.875 * 1872 101.6 1872.5 84.6437 * 1873 66.2 1873.5 54.9688 * 1874 44.7 1874.5 29.8625 * 1875 17 1875.5 12.35 * 1876 11.3 1876.5 12.0563 * 1877 12.4 1877.5 7.80625 * 1878 3.4 1878.5 2.49375 * 1879 6 1879.5 17.9375 * 1880 32.3 1880.5 44.6063 * 1881 54.3 1881.5 58.125 * 1882 59.7 1882.5 62.05 * 1883 63.7 1883.5 64.5563 * 1884 63.5 1884.5 59.5125 * 1885 52.2 1885.5 38.8625 * 1886 25.4 1886.5 17.9688 * 1887 13.1 1887.5 9.2125 * 1888 6.8 1888.5 6.10625 * 1889 6.3 1889.5 4.8875 * 1890 7.1 1890.5 19.0625 * 1891 35.6 1891.5 55.325 * 1892 73 1892.5 81.8312 * 1893 85.1 1893.5 83.1812 * 1894 78 1894.5 71.9437 * 1895 64 1895.5 53 * 1896 41.8 1896.5 32.5812 * 1897 26.2 1897.5 26.3875 * 1898 26.7 1898.5 19.5938 * 1899 12.1 1899.5 10.3125 * 1900 9.5 1900.5 5.79375 * 1901 2.7 1901.5 2.2125 * 1902 5 1902.5 13.7437 * 1903 24.4 1903.5 33.0687 * 1904 42 1904.5 54.4562 * 1905 63.5 1905.5 59.4812 * 1906 53.8 1906.5 58.1375 * 1907 62 1907.5 56.05 * 1908 48.5 1908.5 46.9375 * 1909 43.9 1909.5 31.7687 * 1910 18.6 1910.5 10.7 * 1911 5.7 1911.5 3.98125 * 1912 3.6 1912.5 1.85625 * 1913 1.4 1913.5 3 * 1914 9.6 1914.5 28.4062 * 1915 47.4 1915.5 51.6875 * 1916 57.1 1916.5 82.5625 * 1917 103.9 1917.5 96.2375 * 1918 80.6 1918.5 72.2687 * 1919 63.6 1919.5 50.2563 * 1920 37.6 1920.5 30.9688 * 1921 26.1 1921.5 19.9562 * 1922 14.2 1922.5 8.575 * 1923 5.8 1923.5 9 * 1924 16.7 1924.5 29.9562 * 1925 44.3 1925.5 55.5063 * 1926 63.9 1926.5 67.125 * 1927 69 1927.5 74.525 * 1928 77.8 1928.5 73.725 * 1929 64.9 1929.5 50.4 * 1930 35.7 1930.5 27.2563 * 1931 21.2 1931.5 15.5813 * 1932 11.1 1932.5 7.58125 * 1933 5.7 1933.5 5.15 * 1934 8.7 1934.5 19.8625 * 1935 36.1 1935.5 57.4438 * 1936 79.7 1936.5 100.075 * 1937 114.4 1937.5 115.469 * 1938 109.6 1938.5 100.212 * 1939 88.8 1939.5 78.2687 * 1940 67.8 1940.5 57.3937 * 1941 47.5 1941.5 38.675 * 1942 30.6 1942.5 22.8125 * 1943 16.3 1943.5 10.5813 * 1944 9.6 1944.5 17.2688 * 1945 33.2 1945.5 60.6875 * 1946 92.6 1946.5 126.769 * 1947 151.6 1947.5 147.738 * 1948 136.3 1948.5 137.719 * 1949 134.7 1949.5 110.106 * 1950 83.9 1950.5 75.8438 * 1951 69.4 1951.5 50.6437 * 1952 31.5 1952.5 20.925 * 1953 13.9 1953.5 5.95 * 1954 4.4 1954.5 14.125 * 1955 38 1955.5 88.9188 * 1956 141.7 1956.5 172.769 * 1957 190.2 1957.5 192.144 * 1958 184.8 1958.5 174.481 * 1959 159 1959.5 138.262 * 1960 112.3 Problem 10 Y = 2 + 5*X + 10*N(0,1). X Y * -1.9935 -1.8918 -1.94095 -35.2745 * -1.8884 -8.6202 -1.88485 -2.82353 * -1.8813 -0.4152 -1.87995 -2.47618 * -1.8786 -4.6967 -1.875 -4.73997 * -1.8714 -2.4144 -1.8411 -8.60927 * -1.8108 -21.8853 -1.7361 -24.7487 * -1.6614 -16.5097 -1.63025 -13.5024 * -1.5991 -10.4657 -1.5207 -7.32047 * -1.4423 -4.115 -1.3932 1.73866 * -1.3441 6.5665 -1.25855 -18.8183 * -1.173 -6.7649 -1.16525 1.02751 * -1.1575 8.8276 -1.07305 24.6484 * -0.9886 1.8109 -0.9041 9.6553 * -0.8196 9.6428 -0.79835 9.24076 * -0.7771 -0.6165 -0.77385 -4.52267 * -0.7706 -8.4213 -0.7488 -49.3417 * -0.727 -16.4491 -0.72565 -8.02464 * -0.7243 -0.0667 -0.72355 3.37492 * -0.7228 6.5713 -0.67315 56.7359 * -0.6235 -4.0436 -0.6129 -5.24408 * -0.6023 -6.4194 -0.38365 -3.08358 * -0.165 -1.9114 -0.13835 -6.45606 * -0.1117 -9.5246 -0.08435 -7.10014 * -0.057 -3.2154 0.01765 -1.49184 * 0.0923 0.6541 0.10275 1.83915 * 0.1132 3.0247 0.21445 -2.94489 * 0.3157 2.941 0.325 15.4711 * 0.3343 9.7848 0.33495 7.30446 * 0.3356 4.7713 0.35915 -5.99951 * 0.3827 22.0539 0.3923 14.7341 * 0.4019 7.1301 0.42945 14.3907 * 0.457 22.3302 0.4718 10.5056 * 0.4866 -2.7979 0.54535 -5.65421 * 0.6041 10.2864 0.6422 6.84328 * 0.6803 2.7993 0.7599 6.29874 * 0.8395 12.1989 0.85645 13.7464 * 0.8734 12.3065 0.89245 -7.12485 * 0.9115 -15.3026 0.91525 -11.2272 * 0.919 -6.6749 0.9953 11.67 * 1.0716 -7.0521 1.11825 1.64995 * 1.1649 11.8429 1.1955 18.6319 * 1.2261 22.8325 1.26895 12.5529 * 1.3118 5.2912 1.3301 11.6235 * 1.3484 16.8654 1.3591 16.0035 * 1.3698 14.3045 1.47095 -1.19087 * 1.5721 -0.6553 1.59895 6.84978 * 1.6258 14.1038 1.70035 5.82268 * 1.7749 3.3556 1.79915 14.8538 * 1.8234 26.2797 1.8983 -32.9517 * 1.9732 11.5406 1.9758 20.2991 * 1.9784 28.2522 1.9903 25.8145 * 2.0022 7.7605 2.01265 12.5067 * 2.0231 18.0102 2.03145 148.719 * 2.0398 11.571 2.03995 1.7985 * 2.0401 -8.0188 2.0579 -300.015 * 2.0757 2.5576 2.07905 10.3759 * 2.0824 18.5371 2.14375 52.2431 * 2.2051 12.4771 2.23425 6.386 * 2.2634 2.1298 2.2855 3.91014 * 2.3076 7.2745 2.3368 14.6738 * 2.366 16.3256 2.37955 8.57879 * 2.3931 4.0354 2.4053 12.4432 * 2.4175 23.8374 2.50515 16.8874 * 2.5928 8.5572 2.60815 20.887 * 2.6235 33.2063 2.7172 33.1804 * 2.8109 5.2561 2.85035 13.1836 * 2.8898 18.4409 2.92295 4.48995 * 2.9561 1.5702 2.9615 5.462 * 2.9669 9.5982 3.0415 17.6077 * 3.1161 11.6483 3.12955 16.811 * 3.143 21.7285 3.15895 25.3126 * 3.1749 27.2958 3.2061 25.518 * 3.2373 21.1916 3.32695 16.1386 * 3.4166 15.3527 3.51485 21.7743 * 3.6131 28.2207 3.6383 40.1068 * 3.6635 28.3065 3.6652 24.9403 * 3.6669 21.5368 3.70775 7.90859 * 3.7486 26.4556 3.7508 25.6901 * 3.753 24.8933 3.7696 13.9376 * 3.7862 11.0617 3.79415 20.0226 * 3.8021 28.6064 3.81595 24.3874 * 3.8298 14.577 3.8497 12.86 * 3.8696 15.3088 3.88735 19.501 * 3.9051 23.2952 3.928 21.8433 * 3.9509 18.6796 4.00935 16.4929 * 4.0678 21.0208 4.0858 24.7608 * 4.1038 28.473 4.12975 31.8359 * 4.1557 33.2469 4.20065 22.5816 * 4.2456 21.2484 4.251 23.9213 * 4.2564 26.5592 4.2896 25.6624 * 4.3228 21.2314 4.33155 23.5524 * 4.3403 25.9979 4.378 29.7543 * 4.4157 28.4785 4.45775 22.929 * 4.4998 18.3307 4.53825 22.1874 * 4.5767 27.6318 4.60395 29.9429 * 4.6312 31.1673 4.66705 28.0556 * 4.7029 26.4379 4.7373 35.9088 * 4.7717 43.1573 4.80705 32.6007 * 4.8424 20.1264 4.86695 18.0745 * 4.8915 19.0873 TEST06 Cubic spline interpolation. Problem 1 DeBoor example, Mars position X Y * 1250.5 1.3914 1255.5 1.38603 * 1260.5 1.37696 1265.5 1.3642 * 1270.5 1.34783 1275.5 1.32792 * 1280.5 1.30456 1285.5 1.27784 * 1290.5 1.24787 1295.5 1.21476 * 1300.5 1.17862 1305.5 1.13958 * 1310.5 1.09776 1315.5 1.05331 * 1320.5 1.00636 1325.5 0.957041 * 1330.5 0.90553 1335.5 0.851979 * 1340.5 0.79642 Problem 2 DeBoor example, roughly linear data X Y * 1 0 1.5 0.147883 * 2 0.6 2.5 1.27548 * 3 1.77 3.5 1.80393 * 4 1.92 4.5 2.60628 * 5 3.31 5.5 3.46843 * 6 3.52 6.5 3.96999 * 7 4.59 7.5 5.04535 * 8 5.31 8.5 5.47486 * 9 5.79 9.5 6.42397 * 10 7.06 10.5 7.33302 * 11 7.17 Problem 3 The pulse data, 0 0 0 0 0 1 0 0 0 0 0 X Y * 0 0 0.5 0.00490196 * 1 0 1.5 -0.00980392 * 2 0 2.5 0.0343137 * 3 0 3.5 -0.127451 * 4 0 4.5 0.60049 * 5 1 5.5 0.60049 * 6 0 6.5 -0.127451 * 7 0 7.5 0.0343137 * 8 0 8.5 -0.00980392 * 9 0 9.5 0.00490196 * 10 0 Problem 4 The jump data, 0 0 0 0 0 1/2 1 1 1 1 1 X Y * 0 0 0.5 -0.0711805 * 1 0 1.5 0.142361 * 2 0 2.5 -0.498263 * 3 0 3.5 1.85069 * 4 0 4.495 -6.7242 * 4.99 0 4.995 0.249061 * 5 0.5 5.005 0.750939 * 5.01 1 5.505 7.7242 * 6 1 6.5 -0.850692 * 7 1 7.5 1.49826 * 8 1 8.5 0.857639 * 9 1 9.5 1.07118 * 10 1 Problem 5 DeBoor's Titanium property data X Y * 595 0.644 600 0.626793 * 605 0.622 610 0.628164 * 615 0.638 620 0.644675 * 625 0.649 630 0.652511 * 635 0.652 640 0.645281 * 645 0.639 650 0.639864 * 655 0.646 660 0.653263 * 665 0.657 670 0.654584 * 675 0.652 680 0.6544 * 685 0.655 690 0.648067 * 695 0.644 700 0.652333 * 705 0.663 710 0.664977 * 715 0.663 720 0.664011 * 725 0.668 730 0.67298 * 735 0.676 740 0.675444 * 745 0.676 750 0.681492 * 755 0.686 760 0.683711 * 765 0.679 770 0.677287 * 775 0.678 780 0.679639 * 785 0.683 790 0.688656 * 795 0.694 800 0.696736 * 805 0.699 810 0.7034 * 815 0.71 820 0.718538 * 825 0.73 830 0.745198 * 835 0.763 840 0.783294 * 845 0.812 850 0.854375 * 855 0.907 860 0.967208 * 865 1.044 870 1.15442 * 875 1.336 880 1.60611 * 885 1.881 890 2.07163 * 895 2.169 900 2.17749 * 905 2.075 910 1.85478 * 915 1.598 920 1.38578 * 925 1.211 930 1.05186 * 935 0.916 940 0.814898 * 945 0.746 950 0.702172 * 955 0.672 960 0.646039 * 965 0.627 970 0.61842 * 975 0.615 980 0.610904 * 985 0.607 990 0.605339 * 995 0.606 1000 0.608116 * 1005 0.609 1010 0.606571 * 1015 0.603 1020 0.600976 * 1025 0.601 1030 0.602524 * 1035 0.603 1040 0.600928 * 1045 0.601 1050 0.606765 * 1055 0.611 1060 0.607014 * 1065 0.601 1070 0.600806 * 1075 0.608 Problem 6 The Sawtooth data X Y * 0 0 0.25 0.910478 * 0.5 1 0.75 0.429043 * 1 0 1.125 0.174943 * 1.25 0.5 1.375 0.837072 * 1.5 1 1.625 0.851768 * 1.75 0.5 1.875 0.130857 * 2 0 2.08333 0.129991 * 2.16667 0.333333 2.25 0.496401 * 2.33333 0.666667 2.41667 0.884404 * 2.5 1 2.58333 0.88265 * 2.66667 0.666667 2.75 0.501663 * 2.83333 0.333333 2.91667 0.110697 * 3 0 3.0625 0.0898109 * 3.125 0.25 3.1875 0.387054 * 3.25 0.5 3.3125 0.611972 * 3.375 0.75 3.4375 0.915058 * 3.5 1 3.5625 0.915295 * 3.625 0.75 3.6875 0.611262 * 3.75 0.5 3.8125 0.389655 * 3.875 0.25 3.9375 0.0801165 * 4 0 4.05 0.0720976 * 4.1 0.2 4.15 0.30691 * 4.2 0.4 4.25 0.500261 * 4.3 0.6 4.35 0.692046 * 4.4 0.8 4.45 0.931554 * 4.5 1 4.55 0.931738 * 4.6 0.8 4.65 0.691493 * 4.7 0.6 4.75 0.50229 * 4.8 0.4 4.85 0.299346 * 4.9 0.2 4.95 0.100327 * 5 0 Problem 7 Concavity test data X Y * 0 0 0.05 0.591263 * 0.1 0.9 0.15 0.961224 * 0.2 0.95 0.25 0.995092 * 0.3 0.9 0.35 0.502157 * 0.4 0.1 0.45 -0.0037214 * 0.5 0.05 0.55 0.0627283 * 0.6 0.05 0.7 0.0413918 * 0.8 0.2 0.9 0.519929 * 1 1 Problem 8 Extrapolation test data X Y * 0 0 35.5 0.326902 * 71 7.7554 87.5 13.1944 * 104 19.7062 119.5 26.706 * 135 35.5379 140 39.0902 * 145 42.9154 152.5 49.1693 * 160 54.7752 170.5 60.1962 * 181 66.7587 187 72.4285 * 193 78.4929 199 83.9483 * 205 89.7683 210 95.6393 * 215 101.746 220 107.422 * 225 113.482 231.5 123.143 * 238 135.457 Problem 9 Sunspot data, 1700-1960. X Y * 1700 5 1700.5 8.24884 * 1701 11 1701.5 13.3773 * 1702 16 1702.5 19.3669 * 1703 23 1703.5 27.1552 * 1704 36 1704.5 50.8874 * 1705 58 1705.5 46.0451 * 1706 29 1706.5 22.0573 * 1707 20 1707.5 15.1009 * 1708 10 1708.5 8.41414 * 1709 8 1709.5 5.86754 * 1710 3 1710.5 0.990688 * 1711 0 1711.5 -0.205296 * 1712 0 1712.5 0.455495 * 1713 2 1713.5 5.50831 * 1714 11 1714.5 18.2612 * 1715 27 1715.5 36.8217 * 1716 47 1716.5 56.452 * 1717 63 1717.5 64.4955 * 1718 60 1718.5 49.9411 * 1719 39 1719.5 31.7402 * 1720 28 1720.5 26.4732 * 1721 26 1721.5 25.2419 * 1722 22 1722.5 15.4342 * 1723 11 1723.5 13.7712 * 1724 21 1724.5 29.231 * 1725 40 1725.5 55.8047 * 1726 78 1726.5 104.675 * 1727 122 1727.5 118.37 * 1728 103 1728.5 87.5966 * 1729 73 1729.5 58.3689 * 1730 47 1730.5 41.1778 * 1731 35 1731.5 23.1701 * 1732 11 1732.5 4.892 * 1733 5 1733.5 9.63693 * 1734 16 1734.5 22.5603 * 1735 34 1735.5 53.2469 * 1736 70 1736.5 75.5769 * 1737 81 1737.5 96.6953 * 1738 111 1738.5 111.017 * 1739 101 1739.5 87.9879 * 1740 73 1740.5 56.1566 * 1741 40 1741.5 27.3857 * 1742 20 1742.5 17.9258 * 1743 16 1743.5 10.0363 * 1744 5 1744.5 6.17897 * 1745 11 1745.5 15.9978 * 1746 22 1746.5 30.3298 * 1747 40 1747.5 49.8081 * 1748 60 1748.5 70.8004 * 1749 80.9 1749.5 87.503 * 1750 83.4 1750.5 65.0127 * 1751 47.7 1751.5 45.4462 * 1752 47.8 1752.5 42.0275 * 1753 30.7 1753.5 19.6188 * 1754 12.2 1754.5 10.0097 * 1755 9.6 1755.5 8.12986 * 1756 10.2 1756.5 19.9708 * 1757 32.4 1757.5 41.6118 * 1758 47.6 1758.5 51.607 * 1759 54 1759.5 55.9725 * 1760 62.9 1760.5 77.2779 * 1761 85.9 1761.5 77.1161 * 1762 61.2 1762.5 50.6704 * 1763 45.1 1763.5 41.1022 * 1764 36.4 1764.5 29.4957 * 1765 20.9 1765.5 12.715 * 1766 11.4 1766.5 21.7818 * 1767 37.8 1767.5 52.9452 * 1768 69.8 1768.5 90.4749 * 1769 106.1 1769.5 108.193 * 1770 100.8 1770.5 90.5164 * 1771 81.6 1771.5 75.7167 * 1772 66.5 1772.5 49.3542 * 1773 34.8 1773.5 32.129 * 1774 30.6 1774.5 19.3423 * 1775 7 1775.5 5.42689 * 1776 19.8 1776.5 51.3876 * 1777 92.5 1777.5 132.06 * 1778 154.4 1778.5 148.422 * 1779 125.9 1779.5 102.276 * 1780 84.8 1780.5 76.0493 * 1781 68.1 1781.5 53.6646 * 1782 38.5 1782.5 29.2173 * 1783 22.8 1783.5 15.4912 * 1784 10.2 1784.5 11.518 * 1785 24.1 1785.5 50.2617 * 1786 82.9 1786.5 112.835 * 1787 132 1787.5 135.61 * 1788 130.9 1788.5 125.688 * 1789 118.1 1789.5 105.249 * 1790 89.9 1790.5 76.0028 * 1791 66.6 1791.5 62.9396 * 1792 60 1792.5 53.3136 * 1793 46.9 1793.5 44.5933 * 1794 41 1794.5 31.1882 * 1795 21.3 1795.5 17.6287 * 1796 16 1796.5 11.4593 * 1797 6.4 1797.5 4.10918 * 1798 4.1 1798.5 5.1415 * 1799 6.8 1799.5 9.27481 * 1800 14.5 1800.5 23.7593 * 1801 34 1801.5 41.6006 * 1802 45 1802.5 44.1632 * 1803 43.1 1803.5 45.2215 * 1804 47.5 1804.5 46.3257 * 1805 42.2 1805.5 36.263 * 1806 28.1 1806.5 17.9348 * 1807 10.1 1807.5 8.11043 * 1808 8.1 1808.5 5.77351 * 1809 2.5 1809.5 0.533046 * 1810 0 1810.5 0.469309 * 1811 1.4 1811.5 2.55222 * 1812 5 1812.5 9.24682 * 1813 12.2 1813.5 11.823 * 1814 13.9 1814.5 23.5487 * 1815 35.4 1815.5 42.9696 * 1816 45.8 1816.5 44.8978 * 1817 41.1 1817.5 35.4642 * 1818 30.1 1818.5 26.6579 * 1819 23.9 1819.5 20.2416 * 1820 15.6 1820.5 10.5255 * 1821 6.6 1821.5 4.96881 * 1822 4 1822.5 2.24924 * 1823 1.8 1823.5 4.59673 * 1824 8.5 1824.5 11.5514 * 1825 16.6 1825.5 26.1229 * 1826 36.3 1826.5 43.3072 * 1827 49.6 1827.5 57.7109 * 1828 64.2 1828.5 65.9365 * 1829 67 1829.5 70.8054 * 1830 70.9 1830.5 61.3043 * 1831 47.8 1831.5 37.0525 * 1832 27.5 1832.5 16.8983 * 1833 8.5 1833.5 6.47926 * 1834 13.2 1834.5 30.1221 * 1835 56.9 1835.5 90.8197 * 1836 121.5 1836.5 138.437 * 1837 138.3 1837.5 122.371 * 1838 103.2 1838.5 92.2907 * 1839 85.7 1839.5 76.9158 * 1840 64.6 1840.5 49.646 * 1841 36.7 1841.5 29.4753 * 1842 24.2 1842.5 16.9527 * 1843 10.7 1843.5 9.51387 * 1844 15 1844.5 26.9168 * 1845 40.1 1845.5 50.2564 * 1846 61.5 1846.5 78.3451 * 1847 98.5 1847.5 116.963 * 1848 124.7 1848.5 115.228 * 1849 96.3 1849.5 78.1392 * 1850 66.6 1850.5 64.203 * 1851 64.5 1851.5 60.7612 * 1852 54.1 1852.5 46.9272 * 1853 39 1853.5 29.8299 * 1854 20.6 1854.5 12.7032 * 1855 6.7 1855.5 3.25735 * 1856 4.3 1856.5 11.3049 * 1857 22.7 1857.5 36.8355 * 1858 54.8 1858.5 76.4279 * 1859 93.8 1859.5 99.4903 * 1860 95.8 1860.5 87.2108 * 1861 77.2 1861.5 68.1539 * 1862 59.1 1862.5 49.5112 * 1863 44 1863.5 45.7387 * 1864 47 1864.5 40.3588 * 1865 30.5 1865.5 23.176 * 1866 16.3 1866.5 8.2746 * 1867 7.3 1867.5 20.0881 * 1868 37.6 1868.5 51.7481 * 1869 74 1869.5 112.057 * 1870 139 1870.5 130.999 * 1871 111.2 1871.5 105.223 * 1872 101.6 1872.5 85.5611 * 1873 66.2 1873.5 54.4457 * 1874 44.7 1874.5 30.3186 * 1875 17 1875.5 11.3548 * 1876 11.3 1876.5 12.7622 * 1877 12.4 1877.5 8.28376 * 1878 3.4 1878.5 1.69021 * 1879 6 1879.5 17.5679 * 1880 32.3 1880.5 45.3632 * 1881 54.3 1881.5 58.167 * 1882 59.7 1882.5 61.719 * 1883 63.7 1883.5 64.4571 * 1884 63.5 1884.5 60.14 * 1885 52.2 1885.5 38.7577 * 1886 25.4 1886.5 17.5042 * 1887 13.1 1887.5 9.28796 * 1888 6.8 1888.5 6.51894 * 1889 6.3 1889.5 4.82378 * 1890 7.1 1890.5 18.0109 * 1891 35.6 1891.5 55.8075 * 1892 73 1892.5 82.5092 * 1893 85.1 1893.5 82.8933 * 1894 78 1894.5 71.9552 * 1895 64 1895.5 53.3986 * 1896 41.8 1896.5 31.6505 * 1897 26.2 1897.5 26.8371 * 1898 26.7 1898.5 19.8263 * 1899 12.1 1899.5 9.87011 * 1900 9.5 1900.5 6.46822 * 1901 2.7 1901.5 1.4695 * 1902 5 1902.5 14.0288 * 1903 24.4 1903.5 32.5279 * 1904 42 1904.5 55.322 * 1905 63.5 1905.5 59.2716 * 1906 53.8 1906.5 57.8292 * 1907 62 1907.5 56.3365 * 1908 48.5 1908.5 46.7247 * 1909 43.9 1909.5 32.4897 * 1910 18.6 1910.5 9.77882 * 1911 5.7 1911.5 4.19495 * 1912 3.6 1912.5 2.67886 * 1913 1.4 1913.5 1.37711 * 1914 9.6 1914.5 29.8127 * 1915 47.4 1915.5 50.5596 * 1916 57.1 1916.5 82.5738 * 1917 103.9 1917.5 98.0203 * 1918 80.6 1918.5 70.8702 * 1919 63.6 1919.5 50.7615 * 1920 37.6 1920.5 30.3712 * 1921 26.1 1921.5 20.6162 * 1922 14.2 1922.5 8.45157 * 1923 5.8 1923.5 8.42755 * 1924 16.7 1924.5 29.8382 * 1925 44.3 1925.5 56.307 * 1926 63.9 1926.5 66.7214 * 1927 69 1927.5 74.1575 * 1928 77.8 1928.5 74.7984 * 1929 64.9 1929.5 49.9987 * 1930 35.7 1930.5 26.8067 * 1931 21.2 1931.5 15.8619 * 1932 11.1 1932.5 7.78318 * 1933 5.7 1933.5 5.04289 * 1934 8.7 1934.5 19.3453 * 1935 36.1 1935.5 57.0511 * 1936 79.7 1936.5 100.763 * 1937 114.4 1937.5 116.147 * 1938 109.6 1938.5 99.71 * 1939 88.8 1939.5 78.1875 * 1940 67.8 1940.5 57.4023 * 1941 47.5 1941.5 38.6157 * 1942 30.6 1942.5 23.1849 * 1943 16.3 1943.5 10.6198 * 1944 9.6 1944.5 16.7735 * 1945 33.2 1945.5 58.9488 * 1946 92.6 1946.5 129.256 * 1947 151.6 1947.5 147.288 * 1948 136.3 1948.5 137.715 * 1949 134.7 1949.5 110.415 * 1950 83.9 1950.5 74.8125 * 1951 69.4 1951.5 51.8475 * 1952 31.5 1952.5 20.1099 * 1953 13.9 1953.5 7.46279 * 1954 4.4 1954.5 11.3389 * 1955 38 1955.5 88.5315 * 1956 141.7 1956.5 175.497 * 1957 190.2 1957.5 191.541 * 1958 184.8 1958.5 174.051 * 1959 159 1959.5 138.493 * 1960 112.3 Problem 10 Y = 2 + 5*X + 10*N(0,1). X Y * -1.9935 -1.8918 -1.94095 -888.73 * -1.8884 -8.6202 -1.88485 -2.31259 * -1.8813 -0.4152 -1.87995 -2.46425 * -1.8786 -4.6967 -1.875 -5.46901 * -1.8714 -2.4144 -1.8411 66.6054 * -1.8108 -21.8853 -1.7361 -258.681 * -1.6614 -16.5097 -1.63025 -8.09771 * -1.5991 -10.4657 -1.5207 -26.0095 * -1.4423 -4.115 -1.3932 5.51567 * -1.3441 6.5665 -1.25855 -44.1175 * -1.173 -6.7649 -1.16525 1.02503 * -1.1575 8.8276 -1.07305 56.7104 * -0.9886 1.8109 -0.9041 -39.8193 * -0.8196 9.6428 -0.79835 9.54022 * -0.7771 -0.6165 -0.77385 -4.38269 * -0.7706 -8.4213 -0.7488 -151.082 * -0.727 -16.4491 -0.72565 -8.05971 * -0.7243 -0.0667 -0.72355 3.38442 * -0.7228 6.5713 -0.67315 -353.514 * -0.6235 -4.0436 -0.6129 -4.20812 * -0.6023 -6.4194 -0.38365 -331.216 * -0.165 -1.9114 -0.13835 -6.2905 * -0.1117 -9.5246 -0.08435 -7.03917 * -0.057 -3.2154 0.01765 -12.2792 * 0.0923 0.6541 0.10275 2.24851 * 0.1132 3.0247 0.21445 -1113.94 * 0.3157 2.941 0.325 17.9953 * 0.3343 9.7848 0.33495 7.30455 * 0.3356 4.7713 0.35915 -62.3287 * 0.3827 22.0539 0.3923 16.3734 * 0.4019 7.1301 0.42945 5.27026 * 0.457 22.3302 0.4718 11.2354 * 0.4866 -2.7979 0.54535 -29.6371 * 0.6041 10.2864 0.6422 11.0783 * 0.6803 2.7993 0.7599 -45.4928 * 0.8395 12.1989 0.85645 15.6879 * 0.8734 12.3065 0.89245 -10.0351 * 0.9115 -15.3026 0.91525 -11.2307 * 0.919 -6.6749 0.9953 112.781 * 1.0716 -7.0521 1.11825 -9.40599 * 1.1649 11.8429 1.1955 20.6109 * 1.2261 22.8325 1.26895 8.10586 * 1.3118 5.2912 1.3301 11.5855 * 1.3484 16.8654 1.3591 16.0786 * 1.3698 14.3045 1.47095 -49.1445 * 1.5721 -0.6553 1.59895 7.53786 * 1.6258 14.1038 1.70035 -16.043 * 1.7749 3.3556 1.79915 18.1944 * 1.8234 26.2797 1.8983 -282.356 * 1.9732 11.5406 1.9758 20.1522 * 1.9784 28.2522 1.9903 77.2844 * 2.0022 7.7605 2.01265 -100.948 * 2.0231 18.0102 2.03145 247.381 * 2.0398 11.571 2.03995 1.79847 * 2.0401 -8.0188 2.0579 -1075.45 * 2.0757 2.5576 2.07905 12.5432 * 2.0824 18.5371 2.14375 -398.855 * 2.2051 12.4771 2.23425 22.2178 * 2.2634 2.1298 2.2855 0.58193 * 2.3076 7.2745 2.3368 22.8883 * 2.366 16.3256 2.37955 8.07958 * 2.3931 4.0354 2.4053 12.3487 * 2.4175 23.8374 2.50515 77.1407 * 2.5928 8.5572 2.60815 20.7569 * 2.6235 33.2063 2.7172 39.2399 * 2.8109 5.2561 2.85035 16.1539 * 2.8898 18.4409 2.92295 1.75854 * 2.9561 1.5702 2.9615 5.45919 * 2.9669 9.5982 3.0415 47.7686 * 3.1161 11.6483 3.12955 16.6069 * 3.143 21.7285 3.15895 25.6743 * 3.1749 27.2958 3.2061 24.2521 * 3.2373 21.1916 3.32695 45.8625 * 3.4166 15.3527 3.51485 -118.157 * 3.6131 28.2207 3.6383 46.2765 * 3.6635 28.3065 3.6652 24.9407 * 3.6669 21.5368 3.70775 -38.0388 * 3.7486 26.4556 3.7508 25.7015 * 3.753 24.8933 3.7696 7.9582 * 3.7862 11.0617 3.79415 20.1581 * 3.8021 28.6064 3.81595 26.2594 * 3.8298 14.577 3.8497 8.1022 * 3.8696 15.3088 3.88735 20.7207 * 3.9051 23.2952 3.928 21.7307 * 3.9509 18.6796 4.00935 11.4134 * 4.0678 21.0208 4.0858 24.6535 * 4.1038 28.473 4.12975 33.1435 * 4.1557 33.2469 4.20065 13.9335 * 4.2456 21.2484 4.251 23.9244 * 4.2564 26.5592 4.2896 28.3412 * 4.3228 21.2314 4.33155 23.495 * 4.3403 25.9979 4.378 33.1907 * 4.4157 28.4785 4.45775 21.1369 * 4.4998 18.3307 4.53825 21.5269 * 4.5767 27.6318 4.60395 30.5508 * 4.6312 31.1673 4.66705 26.6143 * 4.7029 26.4379 4.7373 36.2985 * 4.7717 43.1573 4.80705 34.4098 * 4.8424 20.1264 4.86695 16.9965 * 4.8915 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 * 1250.5 1.3914 1255.5 1.38387 * 1260.5 1.37451 1265.5 1.36179 * 1270.5 1.34547 1275.5 1.32562 * 1280.5 1.30232 1285.5 1.27567 * 1290.5 1.24578 1295.5 1.21274 * 1300.5 1.17668 1305.5 1.13773 * 1310.5 1.096 1315.5 1.05164 * 1320.5 1.00479 1325.5 0.955576 * 1330.5 0.90415 1335.5 0.850803 * 1340.5 0.79642 Problem 2 DeBoor example, roughly linear data X Y * 1 0 1.5 0.311875 * 2 0.695 2.5 1.17563 * 3 1.6 3.5 1.84958 * 4 2.12667 4.5 2.61625 * 5 3.11333 5.5 3.40833 * 6 3.66333 6.5 4.06562 * 7 4.53167 7.5 4.93771 * 8 5.27 8.5 5.56146 * 9 5.92167 9.5 6.41729 * 10 6.86667 10.5 7.09083 * 11 7.17 Problem 3 The pulse data, 0 0 0 0 0 1 0 0 0 0 0 X Y * 0 0 0.5 0 * 1 0 1.5 0 * 2 0 2.5 0 * 3 0 3.5 0.0208333 * 4 0.166667 4.5 0.479167 * 5 0.666667 5.5 0.479167 * 6 0.166667 6.5 0.0208333 * 7 0 7.5 0 * 8 0 8.5 0 * 9 0 9.5 0 * 10 0 Problem 4 The jump data, 0 0 0 0 0 1/2 1 1 1 1 1 X Y * 0 0 0.5 0 * 1 0 1.5 0 * 2 0 2.5 0 * 3 0 3.5 0 * 4 0 4.495 0.0104167 * 4.99 0.0833333 4.995 0.260417 * 5 0.5 5.005 0.739583 * 5.01 0.916667 5.505 0.989583 * 6 1 6.5 1 * 7 1 7.5 1 * 8 1 8.5 1 * 9 1 9.5 1 * 10 1 Problem 5 DeBoor's Titanium property data X Y * 595 0.644 600 0.633792 * 605 0.628333 610 0.630687 * 615 0.637167 620 0.643229 * 625 0.647667 630 0.65 * 635 0.649333 640 0.645583 * 645 0.642333 650 0.643 * 655 0.646667 660 0.65125 * 665 0.654333 670 0.654333 * 675 0.653333 680 0.653375 * 685 0.652667 690 0.649833 * 695 0.649 700 0.653729 * 705 0.659833 710 0.662708 * 715 0.663833 720 0.665667 * 725 0.6685 730 0.671896 * 735 0.674667 740 0.676042 * 745 0.677667 750 0.680854 * 755 0.683167 760 0.682271 * 765 0.68 770 0.67875 * 775 0.679 780 0.68075 * 785 0.684 790 0.6885 * 795 0.693 800 0.6965 * 805 0.7 810 0.704813 * 815 0.7115 820 0.720458 * 825 0.732167 830 0.747104 * 835 0.765667 840 0.788792 * 845 0.819667 850 0.861333 * 855 0.914 860 0.979604 * 865 1.06983 870 1.1985 * 875 1.37817 880 1.60842 * 885 1.83817 890 2.01169 * 895 2.10533 900 2.10606 * 905 2.01117 910 1.8304 * 915 1.613 920 1.40829 * 925 1.22633 930 1.06802 * 935 0.936833 940 0.835604 * 945 0.762 950 0.711604 * 955 0.676833 960 0.650792 * 965 0.6325 970 0.621771 * 975 0.615667 980 0.611229 * 985 0.608167 990 0.606729 * 995 0.606667 1000 0.607396 * 1005 0.6075 1010 0.605896 * 1015 0.603667 1020 0.602167 * 1025 0.601667 1030 0.602 * 1035 0.602333 1040 0.602167 * 1045 0.603 1050 0.605833 * 1055 0.607667 1060 0.605938 * 1065 0.603833 1070 0.604854 * 1075 0.608 Problem 6 The Sawtooth data X Y * 0 0 0.25 0.458333 * 0.5 0.666667 0.75 0.489583 * 1 0.25 1.125 0.28125 * 1.25 0.5 1.375 0.729167 * 1.5 0.833333 1.625 0.729167 * 1.75 0.5 1.875 0.267361 * 2 0.138889 2.08333 0.184028 * 2.16667 0.333333 2.25 0.5 * 2.33333 0.666667 2.41667 0.819444 * 2.5 0.888889 2.58333 0.819444 * 2.66667 0.666667 2.75 0.5 * 2.83333 0.333333 2.91667 0.178819 * 3 0.0972222 3.0625 0.137153 * 3.125 0.25 3.1875 0.375 * 3.25 0.5 3.3125 0.625 * 3.375 0.75 3.4375 0.864583 * 3.5 0.916667 3.5625 0.864583 * 3.625 0.75 3.6875 0.625 * 3.75 0.5 3.8125 0.375 * 3.875 0.25 3.9375 0.134375 * 4 0.075 4.05 0.109375 * 4.1 0.2 4.15 0.3 * 4.2 0.4 4.25 0.5 * 4.3 0.6 4.35 0.7 * 4.4 0.8 4.45 0.891667 * 4.5 0.933333 4.55 0.891667 * 4.6 0.8 4.65 0.7 * 4.7 0.6 4.75 0.5 * 4.8 0.4 4.85 0.3 * 4.9 0.2 4.95 0.1 * 5 0 Problem 7 Concavity test data X Y * 0 0 0.05 0.432292 * 0.1 0.758333 0.15 0.905208 * 0.2 0.933333 0.25 0.907292 * 0.3 0.775 0.35 0.5 * 0.4 0.225 0.45 0.0916667 * 0.5 0.0583333 0.55 0.0541667 * 0.6 0.075 0.7 0.141667 * 0.8 0.308333 0.9 0.613542 * 1 1 Problem 8 Extrapolation test data X Y * 0 0 35.5 3.9651 * 71 8.45463 87.5 13.8991 * 104 20.353 119.5 27.5268 * 135 34.1288 140 39.1439 * 145 43.6624 152.5 48.9412 * 160 54.7958 170.5 60.7643 * 181 66.7171 187 72.611 * 193 78.4164 199 84.1357 * 205 89.8854 210 95.7668 * 215 101.706 220 107.822 * 225 115.189 231.5 124.683 * 238 135.457 Problem 9 Sunspot data, 1700-1960. X Y * 1700 5 1700.5 7.97917 * 1701 10.8333 1701.5 13.5208 * 1702 16.3333 1702.5 19.6667 * 1703 24 1703.5 29.8125 * 1704 37.5 1704.5 46.125 * 1705 49.5 1705.5 42.8542 * 1706 32.3333 1706.5 24.8958 * 1707 19.8333 1707.5 15.1458 * 1708 11.3333 1708.5 9.10417 * 1709 7.5 1709.5 5.47917 * 1710 3.33333 1710.5 1.60417 * 1711 0.5 1711.5 0.104167 * 1712 0.333333 1712.5 1.1875 * 1713 3.16667 1713.5 6.79167 * 1714 12.1667 1714.5 19.2292 * 1715 27.6667 1715.5 37 * 1716 46.3333 1716.5 54.5208 * 1717 59.8333 1717.5 60.7292 * 1718 57 1718.5 49.3333 * 1719 40.6667 1719.5 33.8958 * 1720 29.5 1720.5 27.1458 * 1721 25.6667 1721.5 23.8125 * 1722 20.8333 1722.5 16.7917 * 1723 14.5 1723.5 16.625 * 1724 22.5 1724.5 31.0833 * 1725 43.1667 1725.5 59.5208 * 1726 79 1726.5 98.8125 * 1727 111.5 1727.5 110.958 * 1728 101.167 1728.5 87.8542 * 1729 73.6667 1729.5 60.375 * 1730 49.3333 1730.5 41.0417 * 1731 33 1731.5 23.125 * 1732 14 1732.5 8.72917 * 1733 7.83333 1733.5 11 * 1734 17.1667 1734.5 25.5208 * 1735 37 1735.5 51.8542 * 1736 65.8333 1736.5 75.375 * 1737 84.1667 1737.5 95.5625 * 1738 104.333 1738.5 104.792 * 1739 98 1739.5 86.5208 * 1740 72.1667 1740.5 56.6667 * 1741 42.1667 1741.5 30.6042 * 1742 22.6667 1742.5 18.1875 * 1743 14.8333 1743.5 10.7083 * 1744 7.83333 1744.5 8.45833 * 1745 11.8333 1745.5 16.75 * 1746 23.1667 1746.5 31.1875 * 1747 40.3333 1747.5 50.0604 * 1748 60.15 1748.5 70.0854 * 1749 77.8333 1749.5 80.9708 * 1750 77.0333 1750.5 65.5 * 1751 53.6667 1751.5 48.1375 * 1752 44.9333 1752.5 38.8625 * 1753 30.4667 1753.5 21.7521 * 1754 14.85 1754.5 11.2979 * 1755 10.1333 1755.5 10.4167 * 1756 13.8 1756.5 21.6042 * 1757 31.2333 1757.5 39.6708 * 1758 46.1333 1758.5 50.6688 * 1759 54.4167 1759.5 58.7958 * 1760 65.25 1760.5 73.7 * 1761 77.95 1761.5 72.7354 * 1762 62.6333 1762.5 53.4833 * 1763 46.3333 1763.5 40.7625 * 1764 35.2667 1764.5 28.6333 * 1765 21.9 1765.5 17.0229 * 1766 17.3833 1766.5 25.4646 * 1767 38.7333 1767.5 54.0063 * 1768 70.5167 1768.5 87.1729 * 1769 99.1667 1769.5 102.294 * 1770 98.4833 1770.5 90.9958 * 1771 82.2833 1771.5 73.7896 * 1772 63.7333 1772.5 50.8771 * 1773 39.3833 1773.5 32.8688 * 1774 27.3667 1774.5 19.1542 * 1775 13.0667 1775.5 15.4063 * 1776 29.7833 1776.5 57.1729 * 1777 90.7 1777.5 121.342 * 1778 139.333 1778.5 138.004 * 1779 123.8 1779.5 105.596 * 1780 88.8667 1780.5 76.6896 * 1781 65.95 1781.5 53.3208 * 1782 40.8167 1782.5 31.0042 * 1783 23.3167 1783.5 17.1167 * 1784 14.6167 1784.5 18.6375 * 1785 31.5833 1785.5 54.2333 * 1786 81.2833 1786.5 106.202 * 1787 123.633 1787.5 130.16 * 1788 128.95 1788.5 123.935 * 1789 115.533 1789.5 103.781 * 1790 90.7167 1790.5 78.7 * 1791 69.3833 1791.5 63.5125 * 1792 58.9167 1792.5 53.4646 * 1793 48.1 1793.5 43.8125 * 1794 38.7 1794.5 31.1625 * 1795 23.7 1795.5 18.8604 * 1796 15.2833 1796.5 11.2625 * 1797 7.61667 1797.5 5.50625 * 1798 4.93333 1798.5 5.65833 * 1799 7.63333 1799.5 11 * 1800 16.4667 1800.5 24.3188 * 1801 32.5833 1801.5 39.0542 * 1802 42.85 1802.5 43.9125 * 1803 44.15 1803.5 45.2292 * 1804 45.8833 1804.5 44.4646 * 1805 40.7333 1805.5 34.8854 * 1806 27.45 1806.5 19.3521 * 1807 12.7667 1807.5 9.35833 * 1808 7.5 1808.5 5.28958 * 1809 3.01667 1809.5 1.39583 * 1810 0.65 1810.5 0.827083 * 1811 1.76667 1811.5 3.32083 * 1812 5.6 1812.5 8.56042 * 1813 11.2833 1813.5 13.3479 * 1814 17.2 1814.5 24.8312 * 1815 33.55 1815.5 40.0542 * 1816 43.2833 1816.5 43.0042 * 1817 40.05 1817.5 35.5688 * 1818 30.9 1818.5 27.0562 * 1819 23.55 1819.5 19.6917 * 1820 15.4833 1820.5 11.2188 * 1821 7.66667 1821.5 5.44167 * 1822 4.06667 1822.5 3.09375 * 1823 3.28333 1823.5 5.36458 * 1824 8.73333 1824.5 12.8208 * 1825 18.5333 1825.5 26.5583 * 1826 35.2333 1826.5 42.8438 * 1827 49.8167 1827.5 56.6813 * 1828 62.2333 1828.5 65.3771 * 1829 67.1833 1829.5 68.4104 * 1830 66.4 1830.5 58.8458 * 1831 48.2667 1831.5 37.7354 * 1832 27.7167 1832.5 18.5208 * 1833 12.45 1833.5 12.1563 * 1834 19.7 1834.5 36.2979 * 1835 60.3833 1835.5 88.6396 * 1836 113.533 1836.5 127.823 * 1837 129.65 1837.5 120.035 * 1838 106.133 1838.5 94.7417 * 1839 85.1 1839.5 74.9333 * 1840 63.4667 1840.5 50.8292 * 1841 39.2667 1841.5 30.75 * 1842 24.0333 1842.5 17.8 * 1843 13.6667 1843.5 13.6542 * 1844 18.4667 1844.5 27.9062 * 1845 39.4833 1845.5 51.0479 * 1846 64.1 1846.5 80.1 * 1847 96.7 1847.5 110.238 * 1848 115.6 1848.5 109.335 * 1849 96.0833 1849.5 81.9979 * 1850 71.2 1850.5 65.9521 * 1851 63.1167 1851.5 59.0292 * 1852 53.3167 1852.5 46.3833 * 1853 38.45 1853.5 29.825 * 1854 21.35 1854.5 13.9833 * 1855 8.61667 1855.5 6.17292 * 1856 7.76667 1856.5 14.2188 * 1857 24.9833 1857.5 39.1792 * 1858 55.95 1858.5 73.6729 * 1859 87.6333 1859.5 93.6 * 1860 92.3667 1860.5 86.0812 * 1861 77.2833 1861.5 68.2229 * 1862 59.6 1862.5 51.9896 * 1863 47.0167 1863.5 45.4708 * 1864 43.75 1864.5 38.3917 * 1865 30.8833 1865.5 23.5563 * 1866 17.1667 1866.5 12.7271 * 1867 13.85 1867.5 23.3958 * 1868 38.6167 1868.5 56.5229 * 1869 78.7667 1869.5 105.162 * 1870 123.533 1870.5 123.546 * 1871 114.233 1871.5 106.242 * 1872 97.3 1872.5 83.6521 * 1873 68.5167 1873.5 55.6104 * 1874 43.6667 1874.5 31.1792 * 1875 20.6667 1875.5 14.75 * 1876 12.4333 1876.5 11.7812 * 1877 10.7167 1877.5 7.93125 * 1878 5.33333 1878.5 5.43542 * 1879 9.95 1879.5 19.5542 * 1880 31.5833 1880.5 42.8646 * 1881 51.5333 1881.5 56.625 * 1882 59.4667 1882.5 61.5833 * 1883 63 1883.5 63.2813 * 1884 61.65 1884.5 57.2958 * 1885 49.6167 1885.5 38.7792 * 1886 27.8167 1886.5 19.6771 * 1887 14.1 1887.5 10.1958 * 1888 7.76667 1888.5 6.69792 * 1889 6.51667 1889.5 7.30417 * 1890 11.7167 1890.5 22.1125 * 1891 37.0833 1891.5 53.9583 * 1892 68.7833 1892.5 78.1229 * 1893 81.9 1893.5 81.0062 * 1894 76.85 1894.5 70.6854 * 1895 62.6333 1895.5 52.8667 * 1896 42.9 1896.5 34.4729 * 1897 28.8833 1897.5 26.4708 * 1898 24.1833 1898.5 19.3354 * 1899 14.1 1899.5 10.9625 * 1900 8.8 1900.5 6.20208 * 1901 4.21667 1901.5 4.39583 * 1902 7.85 1902.5 15.0188 * 1903 24.1 1903.5 33.2437 * 1904 42.65 1904.5 52.1812 * 1905 58.3 1905.5 58.3729 * 1906 56.7833 1906.5 57.8208 * 1907 58.3833 1907.5 54.9833 * 1908 49.9833 1908.5 45.9542 * 1909 40.45 1909.5 31.0771 * 1910 20.6667 1910.5 12.6333 * 1911 7.5 1911.5 4.87292 * 1912 3.58333 1912.5 2.71458 * 1913 3.13333 1913.5 6.33333 * 1914 14.5333 1914.5 28.5312 * 1915 42.7167 1915.5 52.4375 * 1916 63.2833 1916.5 79.8125 * 1917 92.2167 1917.5 90.9208 * 1918 81.65 1918.5 72.0437 * 1919 62.1 1919.5 50.7146 * 1920 40.0167 1920.5 32.1438 * 1921 26.0333 1921.5 20.2146 * 1922 14.7833 1922.5 10.475 * 1923 9.01667 1923.5 12 * 1924 19.4833 1924.5 30.6813 * 1925 42.9667 1925.5 53.6313 * 1926 61.4833 1926.5 66.225 * 1927 69.6167 1927.5 73.025 * 1928 74.1833 1928.5 70.5583 * 1929 62.1833 1929.5 50.2667 * 1930 38.15 1930.5 28.8479 * 1931 21.9333 1931.5 16.3396 * 1932 11.8833 1932.5 8.67292 * 1933 7.1 1933.5 7.88333 * 1934 12.7667 1934.5 23.2458 * 1935 38.8 1935.5 58.0521 * 1936 78.2167 1936.5 96.0417 * 1937 107.817 1937.5 110.844 * 1938 106.933 1938.5 98.8625 * 1939 88.7667 1939.5 78.3104 * 1940 67.9167 1940.5 57.7354 * 1941 48.0667 1941.5 39.175 * 1942 31.0333 1942.5 23.6625 * 1943 17.5667 1943.5 13.7396 * 1944 14.65 1944.5 22.7771 * 1945 39.1667 1945.5 63.6375 * 1946 92.5333 1946.5 120.544 * 1947 139.217 1947.5 142.688 * 1948 138.583 1948.5 134.76 * 1949 126.5 1949.5 109.031 * 1950 89.95 1950.5 76.9188 * 1951 65.5 1951.5 50.3854 * 1952 34.8833 1952.5 23.2917 * 1953 15.25 1953.5 10.2167 * 1954 11.5833 1954.5 23.5583 * 1955 49.6833 1955.5 90.1604 * 1956 132.5 1956.5 163.677 * 1957 181.217 1957.5 185.952 * 1958 181.4 1958.5 171.04 * 1959 155.517 1959.5 135.215 * 1960 112.3 Problem 10 Y = 2 + 5*X + 10*N(0,1). X Y * -1.9935 -1.8918 -1.94095 -4.94489 * -1.8884 -6.1313 -1.88485 -4.46672 * -1.8813 -2.49628 -1.87995 -2.67934 * -1.8786 -3.60273 -1.875 -3.872 * -1.8714 -6.03993 -1.8411 -12.0854 * -1.8108 -17.7442 -1.7361 -18.6659 * -1.6614 -16.3983 -1.63025 -13.4674 * -1.5991 -10.4146 -1.5207 -7.19374 * -1.4423 -3.3932 -1.3932 0.815706 * -1.3441 2.56435 -1.25855 0.0031125 * -1.173 -1.94425 -1.16525 1.16291 * -1.1575 5.0594 -1.07305 5.15757 * -0.9886 4.28567 -0.9041 5.6593 * -0.8196 6.6276 -0.79835 4.18739 * -0.7771 -0.207417 -0.77385 -4.47241 * -0.7706 -8.45847 -0.7488 -11.9313 * -0.727 -12.3807 -0.72565 -7.95236 * -0.7243 -1.69077 -0.72355 2.68986 * -0.7228 3.69582 -0.67315 1.07606 * -0.6235 -2.67042 -0.6129 -4.91644 * -0.6023 -5.2721 -0.38365 -4.27451 * -0.165 -3.9316 -0.13835 -5.68047 * -0.1117 -7.2042 -0.08435 -6.13078 * -0.057 -3.62202 0.01765 -1.3627 * 0.0923 0.404283 0.10275 1.75704 * 0.1132 2.61565 0.21445 3.07604 * 0.3157 4.09558 0.325 6.2602 * 0.3343 7.80858 0.33495 7.49553 * 0.3356 8.48732 0.35915 13.2061 * 0.3827 16.6862 0.3923 14.5486 * 0.4019 12.1507 0.42945 14.5176 * 0.457 15.6088 0.4718 9.72207 * 0.4866 3.57083 0.54535 4.11177 * 0.6041 6.85783 0.6422 6.46609 * 0.6803 5.61375 0.7599 7.65732 * 0.8395 10.6502 0.85645 11.4817 * 0.8734 7.68705 0.89245 -1.32055 * 0.9115 -9.26313 0.91525 -10.4214 * 0.919 -8.17572 0.9953 -6.6496 * 1.0716 -3.84007 1.11825 2.63221 * 1.1649 10.5253 1.1955 16.5786 * 1.2261 18.0773 1.26895 14.074 * 1.3118 10.1438 1.3301 11.3904 * 1.3484 14.5096 1.3591 15.0322 * 1.3698 12.238 1.47095 7.18543 * 1.5721 4.29785 1.59895 6.81199 * 1.6258 9.85258 1.70035 8.8998 * 1.7749 8.96765 1.79915 14.7345 * 1.8234 20.0025 1.8983 18.7807 * 1.9732 16.7824 1.9758 19.7766 * 1.9784 22.0516 1.9903 17.8717 * 2.0022 12.8841 2.01265 13.1781 * 2.0231 15.2287 2.03145 14.1689 * 2.0398 9.37923 2.03995 2.13059 * 2.0401 -2.9911 2.0579 -1.98957 * 2.0757 3.45812 2.07905 10.2008 * 2.0824 14.8638 2.14375 14.9586 * 2.2051 11.7625 2.23425 7.53688 * 2.2634 4.7118 2.2855 5.10628 * 2.3076 7.92557 2.3368 11.4368 * 2.366 12.7687 2.37955 10.4045 * 2.3931 9.3841 2.4053 13.8741 * 2.4175 17.9904 2.50515 16.2983 * 2.5928 15.2121 2.60815 20.6178 * 2.6235 24.4397 2.7172 18.9924 * 2.8109 12.1119 2.85035 12.0793 * 2.8898 13.4316 2.92295 9.89812 * 2.9561 5.71998 2.9615 5.97838 * 2.9669 8.60188 3.0415 10.666 * 3.1161 12.9867 3.12955 16.7617 * 3.143 20.9764 3.15895 24.175 * 3.1749 25.3505 3.2061 24.0061 * 3.2373 21.2358 3.32695 18.6674 * 3.4166 18.4705 3.51485 21.9101 * 3.6131 26.0903 3.6383 27.8545 * 3.6635 27.1639 3.6652 25.0223 * 3.6669 23.4849 3.70775 24.1047 * 3.7486 25.3754 3.7508 25.2838 * 3.753 22.8484 3.7696 18.3756 * 3.7862 16.2911 3.79415 19.8299 * 3.8021 23.344 3.81595 21.2414 * 3.8298 17.0372 3.8497 15.4016 * 3.8696 16.5179 3.88735 19.1906 * 3.9051 21.1949 3.928 20.8698 * 3.9509 19.8391 4.00935 20.1016 * 4.0678 21.8726 4.0858 24.7976 * 4.1038 28.0266 4.12975 30.4547 * 4.1557 30.4515 4.20065 27.2588 * 4.2456 24.1333 4.251 24.0428 * 4.2564 24.7861 4.2896 23.884 * 4.3228 22.9138 4.33155 23.7773 * 4.3403 25.6169 4.378 26.9275 * 4.4157 26.3738 4.45775 23.5467 * 4.4998 21.5722 4.53825 23.2663 * 4.5767 26.6709 4.60395 29.1072 * 4.6312 29.7898 4.66705 29.0773 * 4.7029 30.0127 4.7373 34.4163 * 4.7717 36.5322 4.80705 31.2719 * 4.8424 23.7917 4.86695 20.065 * 4.8915 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 BETA2 = 0 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". Approximant values stored in "test13_approx.txt". TEST_APPROX_TEST Normal end of execution. 21 April 2020 02:34:38 PM