C 代码 使用范德蒙德计算二维正交规则的权重 矩阵，假设已指定点.rar

26 February 2022 04:20:21 PM QWV_2D_TEST: C version Test the QWV_2D library. TEST01: Compute the weights associated with an interpolatory quadrature rule defined by N=(T+1)*(T+2)/2 points, exact for polynomials of total degree T or less. Degree T = 1 Number of points N = 3 X Interval = [-1,1] Y Interval = [-1,1] Abscissas: 0: 1 -1 1: 1 1 2: -1 1 Weights: 0: 2 1: 0 2: 2 TEST02: Compute the weights associated with an interpolatory quadrature rule defined by N=(T+1)*(T+2)/2 points, exact for polynomials of total degree T or less. X Interval = [-1,1] Y Interval = [-1,1] Degree T = 0 Number of points N = 1 Weights: 0: 4 Degree T = 1 Number of points N = 3 Weights: 0: 1 1: 1 2: 2 Degree T = 2 Number of points N = 6 Weights: 0: 6.661338147750939e-16 1: 0.6666666666666663 2: 2.222222222222222 3: 0.4444444444444444 4: 5.551115123125783e-17 5: 0.6666666666666664 Degree T = 3 Number of points N = 10 Weights: 0: -0.0555555555555548 1: 0.3333333333333331 2: -0.0555555555555558 3: 0.8888888888888886 4: 0.8888888888888893 5: 0.2222222222222224 6: 1.333333333333333 7: 0.222222222222222 8: 0.1111111111111109 9: 0.1111111111111112 Degree T = 4 Number of points N = 15 Weights: 0: -0.008888888888888585 1: 0.08104919101110999 2: 0.06117303121111189 3: 0.3874097078666773 4: 0.6259236254666553 5: 0.05333333333333364 6: 0.07111111111111075 7: 0.9830822022444254 8: 0.5458066866444637 9: 0.3874097078666775 10: 0.6259236254666564 11: 0.05333333333333374 12: -0.008888888888888447 13: 0.08104919101110963 14: 0.06117303121111158 Degree T = 5 Number of points N = 21 Weights: 0: -0.01037037037036959 1: 0.05037037037036875 2: 0.05037037037037086 3: -0.01037037037036983 4: 0.1876963678740793 5: 0.3460933466518655 6: 0.1876963678740777 7: 0.04514390511851783 8: 0.5541130536814711 9: 0.554113053681471 10: 0.045143905118518 11: 0.2804517802740696 12: 0.6376103570518388 13: 0.2804517802740691 14: 0.03189313191851881 15: 0.3288499092814912 16: 0.3288499092814919 17: 0.03189313191851947 18: 0.02074074074074117 19: 0.03851851851851879 20: 0.02074074074074049 Degree T = 6 Number of points N = 28 Weights: 0: -0.003023431594860501 1: 0.01957267632451788 2: 0.02633929313290802 3: 0.01425431928029104 4: 0.100638304632971 5: 0.2208900184526932 6: 0.1743144584714044 7: 0.01209372637944113 8: 0.01934996220710567 9: 0.3245064820875169 10: 0.4027058473592932 11: 0.1677234226317936 12: 0.1953319357827195 13: 0.4489633053035172 14: 0.3721824611057575 15: 0.02479213907785342 16: 0.01934996220710522 17: 0.324506482087515 18: 0.4027058473592958 19: 0.1677234226317934 20: 0.1006383046329746 21: 0.2208900184526933 22: 0.1743144584714026 23: 0.01209372637944108 24: -0.003023431594861847 25: 0.0195726763245173 26: 0.02633929313290827 27: 0.01425431928029166 Degree T = 7 Number of points N = 36 Weights: 0: -0.003287981859414139 1: 0.01337868480725353 2: 0.02063492063491987 3: 0.01337868480725523 4: -0.003287981859409646 5: 0.05949324721886168 6: 0.130647759999358 7: 0.1306477599993601 8: 0.05949324721885186 9: 0.01263869091685717 10: 0.1979944935601064 11: 0.2832184784823696 12: 0.1979944935601116 13: 0.01263869091685773 14: 0.1221817987389781 15: 0.3150266070593566 16: 0.3150266070593479 17: 0.1221817987389802 18: 0.01771365352315162 19: 0.2490926964598241 20: 0.3408041116306955 21: 0.249092696459828 22: 0.01771365352314972 23: 0.0964698630747679 24: 0.2557725606433943 25: 0.2557725606433938 26: 0.09646986307476541 27: 0.008649923133685664 28: 0.1062007918394693 29: 0.1505805844901001 30: 0.1062007918394696 31: 0.008649923133688961 32: 0.006355881462932072 33: 0.01405228180237514 34: 0.0140522818023769 35: 0.006355881462929458 Degree T = 8 Number of points N = 45 Weights: 0: -0.001269841269830927 1: 0.006706089639048144 2: 0.0111145544135314 3: 0.01026455026455006 4: 0.004930678698745009 5: 0.03633146869161083 6: 0.08838322767331991 7: 0.09965911758463455 8: 0.0640018553375568 9: 0.004061629144890239 10: 0.006772486772490917 11: 0.1258344472781497 12: 0.1927501398511158 13: 0.1699470899470928 14: 0.06342599488133693 15: 0.08376332474106821 16: 0.2170841444606959 17: 0.2477307250801732 18: 0.164809804861218 19: 0.0100477182977938 20: 0.01015873015873124 21: 0.1784328991205229 22: 0.2729409493576851 23: 0.2364021164021178 24: 0.08936689226256009 25: 0.08376332474107383 26: 0.2170841444607007 27: 0.2477307250801685 28: 0.1648098048612214 29: 0.01004771829779317 30: 0.006772486772486295 31: 0.1258344472781391 32: 0.1927501398511158 33: 0.1699470899470954 34: 0.06342599488133673 35: 0.03633146869162266 36: 0.08838322767332538 37: 0.09965911758463282 38: 0.06400185533755436 39: 0.00406162914488965 40: -0.001269841269835684 41: 0.006706089639046594 42: 0.01111455441352869 43: 0.01026455026455077 44: 0.004930678698746464 Degree T = 9 Number of points N = 55 Weights: 0: -0.001368606701961306 1: 0.004837977417135961 2: 0.008876308297144659 3: 0.008876308297144041 4: 0.004837977417145839 5: -0.00136860670192919 6: 0.02425285860995682 7: 0.05727330842923978 8: 0.07008257906577886 9: 0.05727330842922721 10: 0.02425285860988861 11: 0.004659404339103048 12: 0.08354521980495082 13: 0.1370796991940038 14: 0.137079699194019 15: 0.0