C 代码 查找一维参数的数据 y（x） 的多项式插值 通过建立和求解线性系统 对于涉及范德蒙德矩阵的多项式系数.rar

12 August 2019 04:04:40 PM VANDERMONDE_INTERP_1D_TEST: C version Test the VANDERMONDE_INTERP_1D library. The QR_SOLVE library is needed. The R8LIB library is needed. This test needs the CONDITION library. This test needs the TEST_INTERP library. VANDERMONDE_COEF_1D_TEST VANDERMONDE_COEF_1D sets the Vandermonde coefficients for 1D interpolation. Interpolation data: 0: 0 24 1: 1 0 2: 2 0 3: 3 0 4: 4 0 Vandermonde interpolant coefficients: 0: 24 1: -50 2: 35 3: -10 4: 1 Vandermonde interpolant polynomial: p(x) = 1 * x^4 -10 * x^3 +35 * x^2 -50 * x +24 VANDERMONDE_MATRIX_1D_TEST VANDERMONDE_MATRIX_1D sets the Vandermonde matrix for 1D interpolation. Vandermonde matrix: Col: 0 1 2 3 Row 0: 1 -1 1 -1 1: 1 2 4 8 2: 1 3 9 27 3: 1 5 25 125 VANDERMONDE_VALUE_1D_TEST VANDERMONDE_VALUE_1D evaluates a Vandermonde interpolant. The polynomial: p(x) = 1 * x^4 -10 * x^3 +35 * x^2 -50 * x +24 X, P(X): 0: 0 24 1: 0.333333 10.8642 2: 0.666667 3.45679 3: 1 0 4: 1.33333 -0.987654 5: 1.66667 -0.691358 6: 2 0 7: 2.33333 0.493827 8: 2.66667 0.493827 9: 3 0 10: 3.33333 -0.691358 11: 3.66667 -0.987654 12: 4 0 13: 4.33333 3.45679 14: 4.66667 10.8642 15: 5 24 TEST01: Interpolate data from TEST_INTERP problem #1 Number of data points = 18 Condition of Vandermonde matrix is 4.77869e+26 L2 interpolation error averaged per interpolant node = 7.59901e-05 Normalized length of piecewise linear interpolant = 3.13553 Normalized length of polynomial interpolant = 559.092 TEST01: Interpolate data from TEST_INTERP problem #2 Number of data points = 18 Condition of Vandermonde matrix is 1.81734e+34 L2 interpolation error averaged per interpolant node = 1408.99 Normalized length of piecewise linear interpolant = 2.66086 Normalized length of polynomial interpolant = 8.8374e+09 TEST01: Interpolate data from TEST_INTERP problem #3 Number of data points = 11 Condition of Vandermonde matrix is 2.49182e+14 L2 interpolation error averaged per interpolant node = 4.43613e-10 Normalized length of piecewise linear interpolant = 1.68472 Normalized length of polynomial interpolant = 4.30657 TEST01: Interpolate data from TEST_INTERP problem #4 Number of data points = 8 Condition of Vandermonde matrix is 735473 L2 interpolation error averaged per interpolant node = 6.98598e-14 Normalized length of piecewise linear interpolant = 3.25908 Normalized length of polynomial interpolant = 5.38186 TEST01: Interpolate data from TEST_INTERP problem #5 Number of data points = 9 Condition of Vandermonde matrix is 1.1583e+07 L2 interpolation error averaged per interpolant node = 5.47696e-12 Normalized length of piecewise linear interpolant = 3.2218 Normalized length of polynomial interpolant = 37.1961 TEST01: Interpolate data from TEST_INTERP problem #6 Number of data points = 49 Condition of Vandermonde matrix is 1.64361e+159 L2 interpolation error averaged per interpolant node = 124.311 Normalized length of piecewise linear interpolant = 2.68209 Normalized length of polynomial interpolant = 21692.6 TEST01: Interpolate data from TEST_INTERP problem #7 Number of data points = 4 Condition of Vandermonde matrix is 475 L2 interpolation error averaged per interpolant node = 2.35514e-16 Normalized length of piecewise linear interpolant = 2.63961 Normalized length of polynomial interpolant = 3.36731 TEST01: Interpolate data from TEST_INTERP problem #8 Number of data points = 12 Condition of Vandermonde matrix is 3.64961e+09 L2 interpolation error averaged per interpolant node = 4.73764e-11 Normalized length of piecewise linear interpolant = 2.31939 Normalized length of polynomial interpolant = 23167 TEST02: VANDERMONDE_INTERP_1D_MATRIX sets the Vandermonde linear system for the interpolating polynomial. Interpolate data from TEST_INTERP problem #1 Number of data points = 18 Data array: Row: 0 1 Col 0: 0 4 1: 1 5 2: 2 6 3: 4 6 4: 5 5 5: 6 3 6: 7 1 7: 8 1 8: 9 1 9: 10 3 10: 11 4 11: 12 4 12: 13 3 13: 14 3 14: 15 4 15: 16 4 16: 17 3 17: 18 0 Created graphics data file "data01.txt". Created graphics interp file "interp01.txt". Created graphics command file "commands01.txt". TEST02: VANDERMONDE_INTERP_1D_MATRIX sets the Vandermonde linear system for the interpolating polynomial. Interpolate data from TEST_INTERP problem #2 Number of data points = 18 Data array: Row: 0 1 Col 0: 0 0 1: 1.34 5 2: 5 8.66 3: 10 10 4: 10.6 10.4 5: 10.7 12 6: 10.705 28.6 7: 10.8 30.2 8: 11.4 30.6 9: 19.6 30.6 10: 20.2 30.2 11: 20.295 28.6 12: 20.3 12 13: 20.4 10.4 14: 21 10 15: 26 8.66 16: 29.66 5 17: 31 0 Created graphics data file "data02.txt". Created graphics interp file "interp02.txt". Created graphics command file "commands02.txt". TEST02: VANDERMONDE_INTERP_1D_MATRIX sets the Vandermonde linear system for the interpolating polynomial. Interpolate data from TEST_INTERP problem #3 Number of data points = 11 Data array: Row: 0 1 Col 0: 0 0 1: 2 10 2: 3 10 3: 5 10 4: 6 10 5: 8 10 6: 9 10.5 7: 11 15 8: 12 50 9: 14 60 10: 15 85 Created graphics data file "data03.txt". Created graphics interp file "interp03.txt". Created graphics command file "commands03.txt". TEST02: VANDERMONDE_INTERP_1D_MATRIX sets the Vandermonde linear system for the interpolating polynomial. Interpolate data from TEST_INTERP problem #4 Number of data points = 8 Data arr