20 March 2018 1:19:03.840 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 = 0.785674 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 = 0.804423 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 2 L2 data approximation error = 36.7573 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 3 L2 data approximation error = 1.97672 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 4 L2 data approximation error = 1.97672 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 5 L2 data approximation error = 51.3192 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 9 L2 data approximation error = 13149.1 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 12 L2 data approximation error = 571.546 Normalized length of piecewise linear interpolant = 3.13553 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 0 L2 data approximation error = 3.35621 Normalized length of piecewise linear interpolant = 2.66086 Normalized length of polynomial approximant = 1.65971 TEST01: Approximate data from TEST_INTERP problem # 2 Number of data points = 18 Using polynomial approximant of degree 1 L2 data approximation error = 3.35621 Normalized length of piecewise linear interpolant = 2.66086 Normalized length of polynomial approximant = 1.65971 TEST01: Approximate data from TEST_INTERP problem # 2 Number of data points = 18 Using polynomial approximant of degree 2 L2 data approximation error = 100.335 Normalized length of piecewise linear interpolant = 2.66086 Normalized length of polynomial approximant = 1.65971 TEST01: Approximate data from TEST_INTERP problem # 2 Number of data points = 18 Using polynomial approximant of degree 3 L2 data approximation error = 2.51953 Normalized length of piecewise linear interpolant = 2.66086 Normalized length of polynomial approximant = 1.63600 TEST01: Approximate data from TEST_INTERP problem # 2 Number of data points = 18 Using polynomial approximant of degree 4 L2 data approximation error = 2.51953 Normalized length of piecewise linear interpolant = 2.66086 Normalized length of polynomial approximant = 1.63023 TEST01: Approximate data from TEST_INTERP problem # 2 Number of data points = 18 Using polynomial approximant of degree 5 L2 data approximation error = 141.125 Normalized length of piecewise linear interpolant = 2.66086 Normalized length of polynomial approximant = 1.62447 TEST01: Approximate data from TEST_INTERP problem # 2 Number of data points = 18 Using polynomial approximant of degree 9 L2 data approximation error = 106510. Normalized length of piecewise linear interpolant = 2.66086 Normalized length of polynomial approximant = 1.60140 TEST01: Approximate data from TEST_INTERP problem # 2 Number of data points = 18 Using polynomial approximant of degree 12 L2 data approximation error = 2671.31 Normalized length of piecewise linear interpolant = 2.66086 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 0 L2 data approximation error = 7.06939 Normalized length of piecewise linear interpolant = 1.68472 Normalized length of polynomial approximant = 1.39201 TEST01: Approximate data from TEST_INTERP problem # 3 Number of data points = 11 Using polynomial approximant of degree 1 L2 data approximation error = 7.85440 Normalized length of piecewise linear interpolant = 1.68472 Normalized length of polynomial approximant = 1.39201 TEST01: Approximate data from TEST_INTERP problem # 3 Number of data points = 11 Using polynomial approximant of degree 2 L2 data approximation error = 15165.9 Normalized length of piecewise linear interpolant = 1.68472 Normalized length of polynomial approximant = 1.39201 TEST01: Approximate data from TEST_INTERP problem # 3 Number of data points = 11 Using polynomial approximant of degree 3 L2 data approximation error = 10.6870 Normalized length of piecewise linear interpolant = 1.68472 Normalized length of polynomial approximant = 1.39201 TEST01: Approximate data from TEST_INTERP problem # 3 Number of data points = 11 Using polynomial approximant of degree 4 L2 data approximation error = 10.6824 Normalized length of piecewise linear interpolant = 1.68472 Normalized length of polynomial approximant = 1.39201 TEST01: Approximate data from TEST_INTERP problem # 3 Number of data points = 11 Using polynomial approximant of degree 5 L2 data approximation error = 10.6934 Normalized length of piecewise linear interpolant = 1.68472 Normalized length of polynomial approximant = 1.39201 TEST01: Approximate data from TEST_INTERP problem # 3 Number of data points = 11 Using polynomial approximant of degree 9 L2 data approximation error = 10.8130 Normalized length of piecewise linear interpolant = 1.68472 Normalized length of polynomial approximant = 1.37757 TEST01: Approximate data from TEST_INTERP problem # 3 Number of data points = 11 Using polynomial approximant of degree 12 L2 data approximation error = 10.8179 Normalized length of piecewise linear interpolant = 1.68472 Normalized length of polynomial approximant = 1.37345 TEST01: Approximate data from TEST_INTERP problem # 4 Number of data points = 8 Using polynomial approximant of degree 0 L2 data approximation error = 0.171560 Normalized length of piecewise linear interpolant = 3.25908 Normalized length of polynomial approximant = 81.6223 TEST01: Approximate data from TEST_INTERP problem # 4 Number of data points = 8 Using polynomial approximant of degree 1 L2 data approximation error = 0.172436 Normalized length of piecewise linear interpolant = 3.25908 Normalized length of polynomial approximant = 81.6223 TEST01: Approximate data from TEST_INTERP problem # 4 Number of data points = 8 Using polynomial approximant of degree 2 L2 data approximation error = 0.172436 Normalized length of piecewise linear interpolant = 3.25908 Normalized length of polynomial approximant = 81.6223 TEST01: Approximate data from TEST_INTERP problem # 4 Number of data points = 8 Using polynomial approximant of degree 3 L2 data approximation error = 6414.18 Normalized length of piecewise linear interpolant = 3.25908 Normalized length of polynomial approximant = 81.6223 TEST01: Approximate data from TEST_INTERP problem # 4 Number of data points = 8 Using polynomial approximant of degree 4 L2 data approximation error = 0.172436 Normalized length of piecewise linear interpolant = 3.25908 Normalized length of polynomial approximant = 81.6223 TEST01: Approximate data from TEST_INTERP problem # 4 Number of data points = 8 Using polynomial approximant of degree 5 L2 data approximation error = 0.172436 Normalized length of piecewise linear interpolant = 3.25908 Normalized length of polynomial approximant = 81.6223 TEST01: Approximate data from TEST_INTERP problem # 4 Number of data points = 8 Using polynomial approximant of degree 9 L2 data approximation error = 0.306301 Normalized length of piecewise linear interpolant = 3.25908 Normalized length of polynomial approximant = 81.6223 TEST01: Approximate data from TEST_INTERP problem # 4 Number of data points = 8 Using polynomial approximant of degree 12 L2 data approximation error = 0.172436 Normalized length of piecewise linear interpolant = 3.25908 Normalized length of polynomial approximant = 81.6223 TEST01: Approximate data from TEST_INTERP problem # 5 Number of data points = 9 Using polynomial approximant of degree 0 L2 data approximation error = 0.144913 Normalized length of piecewise linear interpolant = 3.22180 Normalized length of polynomial approximant = 81.6223 TEST01: Approximate data from TEST_INTERP problem # 5 Number of data points = 9 Using polynomial approximant of degree 1 L2 data approximation error = 0.164377 Normalized length of piecewise linear interpolant = 3.22180 Normalized length of polynomial approximant = 81.6223 TEST01: Approximate data from TEST_INTERP problem # 5 Number of data points = 9 Using polynomial approximant of degree 2 L2 data approximation error = 0.164377 Normalized length of piecewise linear interpolant = 3.22180 Normalized length of polynomial approximant = 81.6223 TEST01: Approximate data from TEST_INTERP problem # 5 Number of data points = 9 Using polynomial approximant of degree 3 L2 data approximation error = 43.3098 Normalized length of piecewise linear interpolant = 3.22180 Normalized length of polynomial approximant = 81.6223 TEST01: Approximate data from TEST_INTERP problem # 5 Number of data points = 9 Using polynomial approximant of degree 4 L2 data approximation error = 0.164377 Normalized length of piecewise linear interpolant = 3.22180 Normalized length of polynomial approximant = 81.6223 TEST01: Approximate data from TEST_INTERP problem # 5 Number of data points = 9 Using polynomial approximant of degree 5 L2 data approximation error = 0.164377 Normalized length of piecewise linear interpolant = 3.22180 Normalized length of polynomial approximant = 81.6223 TEST01: Approximate data from TEST_INTERP problem # 5 Number of data points = 9 Using polynomial approximant of degree 9 L2 data approximation error = 0.164377 Normalized length of piecewise linear interpolant = 3.22180 Normalized length of polynomial approximant = 81.6223 TEST01: Approximate data from TEST_INTERP problem # 5 Number of data points = 9 Using polynomial approximant of degree 12 L2 data approximation error = 0.164377 Normalized length of piecewise linear interpolant = 3.22180 Normalized length of polynomial approximant = 81.2293 TEST01: Approximate data from TEST_INTERP problem # 6 Number of data points = 49 Using polynomial approximant of degree 0 L2 data approximation error = 0.114942 Normalized length of piecewise linear interpolant = 2.68209 Normalized length of polynomial approximant = 23.8490 TEST01: Approximate data from TEST_INTERP problem # 6 Number of data points = 49 Using polynomial approximant of degree 1 L2 data approximation error = 15.0307 Normalized length of piecewise linear interpolant = 2.68209 Normalized length of polynomial approximant = 21.9694 TEST01: Approximate data from TEST_INTERP problem # 6 Number of data points = 49 Using polynomial approximant of degree 2 L2 data approximation error = 18.3533 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 3 L2 data approximation error = 14227.5 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 4 L2 data approximation error = 0.112608E+08 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 5 L2 data approximation error = 0.915707E+10 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 9 L2 data approximation error = 0.527545E+22 Normalized length of piecewise linear interpolant = 2.68209 Normalized length of polynomial approximant = 3.17486 TEST01: Approximate data from TEST_INTERP problem # 6 Number of data points = 49 Using polynomial approximant of degree 12 L2 data approximation error = 0.428460E+31 Normalized length of piecewise linear interpolant = 2.68209 Normalized length of polynomial approximant = 5161.54 TEST01: Approximate data from TEST_INTERP problem # 7 Number of data points = 4 Using polynomial approximant of degree 0 L2 data approximation error = 0.695971 Normalized length of piecewise linear interpolant = 2.63961 Normalized length of polynomial approximant = 0.425869E+37 TEST01: Approximate data from TEST_INTERP problem # 7 Number of data points = 4 Using polynomial approximant of degree 1 L2 data approximation error = 178.251 Normalized length of piecewise linear interpolant = 2.63961 Normalized length of polynomial approximant = 0.425869E+37 TEST01: Approximate data from TEST_INTERP problem # 7 Number of data points = 4 Using polynomial approximant of degree 2 L2 data approximation error = 190.751 Normalized length of piecewise linear interpolant = 2.63961 Normalized length of polynomial approximant = 0.425869E+37 TEST01: Approximate data from TEST_INTERP problem # 7 Number of data points = 4 Using polynomial approximant of degree 3 L2 data approximation error = 0.790569 Normalized length of piecewise linear interpolant = 2.63961 Normalized length of polynomial approximant = 0.425869E+37 TEST01: Approximate data from TEST_INTERP problem # 7 Number of data points = 4 Using polynomial approximant of degree 4 L2 data approximation error = 0.790569 Normalized length of piecewise linear interpolant = 2.63961 Normalized length of polynomial approximant = 0.425869E+37 TEST01: Approximate data from TEST_INTERP problem # 7 Number of data points = 4 Using polynomial approximant of degree 5 L2 data approximation error = 0.612372 Normalized length of piecewise linear interpolant = 2.63961 Normalized length of polynomial approximant = 0.425869E+37 TEST01: Approximate data from TEST_INTERP problem # 7 Number of data points = 4 Using polynomial approximant of degree 9 L2 data approximation error = 0.790569 Normalized length of piecewise linear interpolant = 2.63961 Normalized length of polynomial approximant = 0.425869E+37 TEST01: Approximate data from TEST_INTERP problem # 7 Number of data points = 4 Using polynomial approximant of degree 12 L2 data approximation error = 1.06428 Normalized length of piecewise linear interpolant = 2.63961 Normalized length of polynomial approximant = 0.425869E+37 TEST01: Approximate data from TEST_INTERP problem # 8 Number of data points = 12 Using polynomial approximant of degree 0 L2 data approximation error = 0.132096 Normalized length of piecewise linear interpolant = 2.31939 Normalized length of polynomial approximant = 0.425869E+37 TEST01: Approximate data from TEST_INTERP problem # 8 Number of data points = 12 Using polynomial approximant of degree 1 L2 data approximation error = 0.210411 Normalized length of piecewise linear interpolant = 2.31939 Normalized length of polynomial approximant = 0.425869E+37 TEST01: Approximate data from TEST_INTERP problem # 8 Number of data points = 12 Using polynomial approximant of degree 2 L2 data approximation error = 0.147601 Normalized length of piecewise linear interpolant = 2.31939 Normalized length of polynomial approximant = 0.425869E+37 TEST01: Approximate data from TEST_INTERP problem # 8 Number of data points = 12 Using polynomial approximant of degree 3 L2 data approximation error = 0.147567 Normalized length of piecewise linear interpolant = 2.31939 Normalized length of polynomial approximant = 0.425869E+37 TEST01: Approximate data from TEST_INTERP problem # 8 Number of data points = 12 Using polynomial approximant of degree 4 L2 data approximation error = 0.147555 Normalized length of piecewise linear interpolant = 2.31939 Normalized length of polynomial approximant = 0.425869E+37 TEST01: Approximate data from TEST_INTERP problem # 8 Number of data points = 12 Using polynomial approximant of degree 5 L2 data approximation error = 0.228450 Normalized length of piecewise linear interpolant = 2.31939 Normalized length of polynomial approximant = 0.425869E+37 TEST01: Approximate data from TEST_INTERP problem # 8 Number of data points = 12 Using polynomial approximant of degree 9 L2 data approximation error = 0.147554 Normalized length of piecewise linear interpolant = 2.31939 Normalized length of polynomial approximant = 0.425869E+37 TEST01: Approximate data from TEST_INTERP problem # 8 Number of data points = 12 Using polynomial approximant of degree 12 L2 data approximation error = 0.147556 Normalized length of piecewise linear interpolant = 2.31939 Normalized length of polynomial approximant = 0.425859E+37 VANDERMONDE_APPROX_1D_TEST: Normal end of execution. 20 March 2018 1:19:03.842 PM