11 September 2021 2:08:11.082 PM VANDERMONDE_APPROX_1D_TEST: FORTRAN90 version Test the VANDERMONDE_APPROX_1D library. The R8LIB library is needed. The QR_SOLVE library is needed. The test needs the CONDITION library. The test needs the TEST_INTERP libary. TEST01: Approximate data from TEST_INTERP problem # 1 Number of data points = 18 Using polynomial approximant of degree 0 L2 data approximation error = 0.392837 Normalized length of piecewise linear interpolant = 3.13553 Normalized length of polynomial approximant = 1.00000 TEST01: Approximate data from TEST_INTERP problem # 1 Number of data points = 18 Using polynomial approximant of degree 1 L2 data approximation error = 0.350074 Normalized length of piecewise linear interpolant = 3.13553 Normalized length of polynomial approximant = 1.08357 TEST01: Approximate data from TEST_INTERP problem # 1 Number of data points = 18 Using polynomial approximant of degree 2 L2 data approximation error = 0.344057 Normalized length of piecewise linear interpolant = 3.13553 Normalized length of polynomial approximant = 1.12211 TEST01: Approximate data from TEST_INTERP problem # 1 Number of data points = 18 Using polynomial approximant of degree 3 L2 data approximation error = 0.332868 Normalized length of piecewise linear interpolant = 3.13553 Normalized length of polynomial approximant = 1.31026 TEST01: Approximate data from TEST_INTERP problem # 1 Number of data points = 18 Using polynomial approximant of degree 4 L2 data approximation error = 0.199123 Normalized length of piecewise linear interpolant = 3.13553 Normalized length of polynomial approximant = 2.51647 TEST01: Approximate data from TEST_INTERP problem # 1 Number of data points = 18 Using polynomial approximant of degree 5 L2 data approximation error = 0.190907 Normalized length of piecewise linear interpolant = 3.13553 Normalized length of polynomial approximant = 2.60932 TEST01: Approximate data from TEST_INTERP problem # 1 Number of data points = 18 Using polynomial approximant of degree 9 L2 data approximation error = 0.613776E-01 Normalized length of piecewise linear interpolant = 3.13553 Normalized length of polynomial approximant = 3.22044 TEST01: Approximate data from TEST_INTERP problem # 1 Number of data points = 18 Using polynomial approximant of degree 12 L2 data approximation error = 0.374634E-01 Normalized length of piecewise linear interpolant = 3.13553 Normalized length of polynomial approximant = 3.37935 TEST01: Approximate data from TEST_INTERP problem # 2 Number of data points = 18 Using polynomial approximant of degree 0 L2 data approximation error = 2.58162 Normalized length of piecewise linear interpolant = 2.66086 Normalized length of polynomial approximant = 1.00000 TEST01: Approximate data from TEST_INTERP problem # 2 Number of data points = 18 Using polynomial approximant of degree 1 L2 data approximation error = 2.58162 Normalized length of piecewise linear interpolant = 2.66086 Normalized length of polynomial approximant = 1.00000 TEST01: Approximate data from TEST_INTERP problem # 2 Number of data points = 18 Using polynomial approximant of degree 2 L2 data approximation error = 1.80946 Normalized length of piecewise linear interpolant = 2.66086 Normalized length of polynomial approximant = 1.88131 TEST01: Approximate data from TEST_INTERP problem # 2 Number of data points = 18 Using polynomial approximant of degree 3 L2 data approximation error = 1.80946 Normalized length of piecewise linear interpolant = 2.66086 Normalized length of polynomial approximant = 1.88131 TEST01: Approximate data from TEST_INTERP problem # 2 Number of data points = 18 Using polynomial approximant of degree 4 L2 data approximation error = 1.76341 Normalized length of piecewise linear interpolant = 2.66086 Normalized length of polynomial approximant = 1.90124 TEST01: Approximate data from TEST_INTERP problem # 2 Number of data points = 18 Using polynomial approximant of degree 5 L2 data approximation error = 1.76341 Normalized length of piecewise linear interpolant = 2.66086 Normalized length of polynomial approximant = 1.90124 TEST01: Approximate data from TEST_INTERP problem # 2 Number of data points = 18 Using polynomial approximant of degree 9 L2 data approximation error = 1.30404 Normalized length of piecewise linear interpolant = 2.66086 Normalized length of polynomial approximant = 8.90486 TEST01: Approximate data from TEST_INTERP problem # 2 Number of data points = 18 Using polynomial approximant of degree 12 L2 data approximation error = 0.894360 Normalized length of piecewise linear interpolant = 2.66086 Normalized length of polynomial approximant = 7153.58 TEST01: Approximate data from TEST_INTERP problem # 3 Number of data points = 11 Using polynomial approximant of degree 0 L2 data approximation error = 7.87737 Normalized length of piecewise linear interpolant = 1.68472 Normalized length of polynomial approximant = 1.00000 TEST01: Approximate data from TEST_INTERP problem # 3 Number of data points = 11 Using polynomial approximant of degree 1 L2 data approximation error = 4.46790 Normalized length of piecewise linear interpolant = 1.68472 Normalized length of polynomial approximant = 1.28026 TEST01: Approximate data from TEST_INTERP problem # 3 Number of data points = 11 Using polynomial approximant of degree 2 L2 data approximation error = 2.59431 Normalized length of piecewise linear interpolant = 1.68472 Normalized length of polynomial approximant = 1.48631 TEST01: Approximate data from TEST_INTERP problem # 3 Number of data points = 11 Using polynomial approximant of degree 3 L2 data approximation error = 1.74627 Normalized length of piecewise linear interpolant = 1.68472 Normalized length of polynomial approximant = 1.58943 TEST01: Approximate data from TEST_INTERP problem # 3 Number of data points = 11 Using polynomial approximant of degree 4 L2 data approximation error = 1.68297 Normalized length of piecewise linear interpolant = 1.68472 Normalized length of polynomial approximant = 1.61226 TEST01: Approximate data from TEST_INTERP problem # 3 Number of data points = 11 Using polynomial approximant of degree 5 L2 data approximation error = 1.66663 Normalized length of piecewise linear interpolant = 1.68472 Normalized length of polynomial approximant = 1.59507 TEST01: Approximate data from TEST_INTERP problem # 3 Number of data points = 11 Using polynomial approximant of degree 9 L2 data approximation error = 0.328589 Normalized length of piecewise linear interpolant = 1.68472 Normalized length of polynomial approximant = 3.28924 TEST01: Approximate data from TEST_INTERP problem # 3 Number of data points = 11 Using polynomial approximant of degree 12 L2 data approximation error = 0.324433E-09 Normalized length of piecewise linear interpolant = 1.68472 Normalized length of polynomial approximant = 3.88345 TEST01: Approximate data from TEST_INTERP problem # 4 Number of data points = 8 Using polynomial approximant of degree 0 L2 data approximation error = 0.149984 Normalized length of piecewise linear interpolant = 3.25908 Normalized length of polynomial approximant = 1.00000 TEST01: Approximate data from TEST_INTERP problem # 4 Number of data points = 8 Using polynomial approximant of degree 1 L2 data approximation error = 0.146011 Normalized length of piecewise linear interpolant = 3.25908 Normalized length of polynomial approximant = 1.02803 TEST01: Approximate data from TEST_INTERP problem # 4 Number of data points = 8 Using polynomial approximant of degree 2 L2 data approximation error = 0.145980 Normalized length of piecewise linear interpolant = 3.25908 Normalized length of polynomial approximant = 1.03194 TEST01: Approximate data from TEST_INTERP problem # 4 Number of data points = 8 Using polynomial approximant of degree 3 L2 data approximation error = 0.559589E-01 Normalized length of piecewise linear interpolant = 3.25908 Normalized length of polynomial approximant = 3.33040 TEST01: Approximate data from TEST_INTERP problem # 4 Number of data points = 8 Using polynomial approximant of degree 4 L2 data approximation error = 0.559577E-01 Normalized length of piecewise linear interpolant = 3.25908 Normalized length of polynomial approximant = 3.32957 TEST01: Approximate data from TEST_INTERP problem # 4 Number of data points = 8 Using polynomial approximant of degree 5 L2 data approximation error = 0.829484E-02 Normalized length of piecewise linear interpolant = 3.25908 Normalized length of polynomial approximant = 3.58478 TEST01: Approximate data from TEST_INTERP problem # 4 Number of data points = 8 Using polynomial approximant of degree 9 L2 data approximation error = 0.177715E-13 Normalized length of piecewise linear interpolant = 3.25908 Normalized length of polynomial approximant = 4.81669 TEST01: Approximate data from TEST_INTERP problem # 4 Number of data points = 8 Using polynomial approximant of degree 12 L2 data approximation error = 0.651592E-14 Normalized length of piecewise linear interpolant = 3.25908 Normalized length of polynomial approximant = 4.89584 TEST01: Approximate data from TEST_INTERP problem # 5 Number of data points = 9 Using polynomial approximant of degree 0 L2 data approximation error = 0.143324 Normalized length of piecewise linear interpolant = 3.22180 Normalized length of polynomial approximant = 1.00000 TEST01: Approximate data from TEST_INTERP problem # 5 Number of data points = 9 Using polynomial approximant of degree 1 L2 data approximation error = 0.143322 Normalized length of piecewise linear interpolant = 3.22180 Normalized length of polynomial approximant = 1.00003 TEST01: Approximate data from TEST_INTERP problem # 5 Number of data points = 9 Using polynomial approximant of degree 2 L2 data approximation error = 0.135170 Normalized length of piecewise linear interpolant = 3.22180 Normalized length of polynomial approximant = 1.31038 TEST01: Approximate data from TEST_INTERP problem # 5 Number of data points = 9 Using polynomial approximant of degree 3 L2 data approximation error = 0.717904E-01 Normalized length of piecewise linear interpolant = 3.22180 Normalized length of polynomial approximant = 3.05546 TEST01: Approximate data from TEST_INTERP problem # 5 Number of data points = 9 Using polynomial approximant of degree 4 L2 data approximation error = 0.391096E-01 Normalized length of piecewise linear interpolant = 3.22180 Normalized length of polynomial approximant = 3.42544 TEST01: Approximate data from TEST_INTERP problem # 5 Number of data points = 9 Using polynomial approximant of degree 5 L2 data approximation error = 0.358900E-01 Normalized length of piecewise linear interpolant = 3.22180 Normalized length of polynomial approximant = 3.41454 TEST01: Approximate data from TEST_INTERP problem # 5 Number of data points = 9 Using polynomial approximant of degree 9 L2 data approximation error = 0.199908E-11 Normalized length of piecewise linear interpolant = 3.22180 Normalized length of polynomial approximant = 47.9536 TEST01: Approximate data from TEST_INTERP problem # 5 Number of data points = 9 Using polynomial approximant of degree 12 L2 data approximation error = 0.615052E-12 Normalized length of piecewise linear interpolant = 3.22180 Normalized length of polynomial approximant = 125.388 TEST01: Approximate data from TEST_INTERP problem # 6 Number of data points = 49 Using polynomial approximant of degree 0 L2 data approximation error = 0.530251E-01 Normalized length of piecewise linear interpolant = 2.68209 Normalized length of polynomial approximant = 1.00000 TEST01: Approximate data from TEST_INTERP problem # 6 Number of data points = 49 Using polynomial approximant of degree 1 L2 data approximation error = 0.525121E-01 Normalized length of piecewise linear interpolant = 2.68209 Normalized length of polynomial approximant = 1.00620 TEST01: Approximate data from TEST_INTERP problem # 6 Number of data points = 49 Using polynomial approximant of degree 2 L2 data approximation error = 0.473605E-01 Normalized length of piecewise linear interpolant = 2.68209 Normalized length of polynomial approximant = 1.24020 TEST01: Approximate data from TEST_INTERP problem # 6 Number of data points = 49 Using polynomial approximant of degree 3 L2 data approximation error = 0.437687E-01 Normalized length of piecewise linear interpolant = 2.68209 Normalized length of polynomial approximant = 1.43902 TEST01: Approximate data from TEST_INTERP problem # 6 Number of data points = 49 Using polynomial approximant of degree 4 L2 data approximation error = 0.424429E-01 Normalized length of piecewise linear interpolant = 2.68209 Normalized length of polynomial approximant = 1.51608 TEST01: Approximate data from TEST_INTERP problem # 6 Number of data points = 49 Using polynomial approximant of degree 5 L2 data approximation error = 0.363054E-01 Normalized length of piecewise linear interpolant = 2.68209 Normalized length of polynomial approximant = 1.97702 TEST01: Approximate data from TEST_INTERP problem # 6 Number of data points = 49 Using polynomial approximant of degree 9 L2 data approximation error = 0.272317E-01 Normalized length of piecewise linear interpolant = 2.68209 Normalized length of polynomial approximant = 2.51535 TEST01: Approximate data from TEST_INTERP problem # 6 Number of data points = 49 Using polynomial approximant of degree 12 L2 data approximation error = 0.187600E-01 Normalized length of piecewise linear interpolant = 2.68209 Normalized length of polynomial approximant = 2.95947 TEST01: Approximate data from TEST_INTERP problem # 7 Number of data points = 4 Using polynomial approximant of degree 0 L2 data approximation error = 0.250000 Normalized length of piecewise linear interpolant = 2.63961 Normalized length of polynomial approximant = 1.00000 TEST01: Approximate data from TEST_INTERP problem # 7 Number of data points = 4 Using polynomial approximant of degree 1 L2 data approximation error = 0.250000 Normalized length of piecewise linear interpolant = 2.63961 Normalized length of polynomial approximant = 1.00000 TEST01: Approximate data from TEST_INTERP problem # 7 Number of data points = 4 Using polynomial approximant of degree 2 L2 data approximation error = 0.590092E-15 Normalized length of piecewise linear interpolant = 2.63961 Normalized length of polynomial approximant = 3.36731 TEST01: Approximate data from TEST_INTERP problem # 7 Number of data points = 4 Using polynomial approximant of degree 3 L2 data approximation error = 0.235514E-15 Normalized length of piecewise linear interpolant = 2.63961 Normalized length of polynomial approximant = 3.36731 TEST01: Approximate data from TEST_INTERP problem # 7 Number of data points = 4 Using polynomial approximant of degree 4 L2 data approximation error = 0.101829E-14 Normalized length of piecewise linear interpolant = 2.63961 Normalized length of polynomial approximant = 3.58258 TEST01: Approximate data from TEST_INTERP problem # 7 Number of data points = 4 Using polynomial approximant of degree 5 L2 data approximation error = 0.129235E-14 Normalized length of piecewise linear interpolant = 2.63961 Normalized length of polynomial approximant = 3.90825 TEST01: Approximate data from TEST_INTERP problem # 7 Number of data points = 4 Using polynomial approximant of degree 9 L2 data approximation error = 0.534437E-14 Normalized length of piecewise linear interpolant = 2.63961 Normalized length of polynomial approximant = 6.52763 TEST01: Approximate data from TEST_INTERP problem # 7 Number of data points = 4 Using polynomial approximant of degree 12 L2 data approximation error = 0.216022E-13 Normalized length of piecewise linear interpolant = 2.63961 Normalized length of polynomial approximant = 10.4248 TEST01: Approximate data from TEST_INTERP problem # 8 Number of data points = 12 Using polynomial approximant of degree 0 L2 data approximation error = 0.101554 Normalized length of piecewise linear interpolant = 2.31939 Normalized length of polynomial approximant = 1.00000 TEST01: Approximate data from TEST_INTERP problem # 8 Number of data points = 12 Using polynomial approximant of degree 1 L2 data approximation error = 0.101522 Normalized length of piecewise linear interpolant = 2.31939 Normalized length of polynomial approximant = 1.00042 TEST01: Approximate data from TEST_INTERP problem # 8 Number of data points = 12 Using polynomial approximant of degree 2 L2 data approximation error = 0.762201E-03 Normalized length of piecewise linear interpolant = 2.31939 Normalized length of polynomial approximant = 2.31944 TEST01: Approximate data from TEST_INTERP problem # 8 Number of data points = 12 Using polynomial approximant of degree 3 L2 data approximation error = 0.748027E-03 Normalized length of piecewise linear interpolant = 2.31939 Normalized length of polynomial approximant = 2.31959 TEST01: Approximate data from TEST_INTERP problem # 8 Number of data points = 12 Using polynomial approximant of degree 4 L2 data approximation error = 0.731706E-03 Normalized length of piecewise linear interpolant = 2.31939 Normalized length of polynomial approximant = 2.32028 TEST01: Approximate data from TEST_INTERP problem # 8 Number of data points = 12 Using polynomial approximant of degree 5 L2 data approximation error = 0.704364E-03 Normalized length of piecewise linear interpolant = 2.31939 Normalized length of polynomial approximant = 2.32052 TEST01: Approximate data from TEST_INTERP problem # 8 Number of data points = 12 Using polynomial approximant of degree 9 L2 data approximation error = 0.627667E-03 Normalized length of piecewise linear interpolant = 2.31939 Normalized length of polynomial approximant = 2.32096 TEST01: Approximate data from TEST_INTERP problem # 8 Number of data points = 12 Using polynomial approximant of degree 12 L2 data approximation error = 0.591022E-10 Normalized length of piecewise linear interpolant = 2.31939 Normalized length of polynomial approximant = 23167.0 VANDERMONDE_APPROX_1D_TEST: Normal end of execution. 11 September 2021 2:08:11.084 PM