A new form of trigonometric orthogonality and Gaussian-type quadrature
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摘要
Gauss's (2n+1)-point trigonometric interpolation formula, based upon f(xi), i = 1(1)2n+1, gives a trigonometric sum of the nth order, S2n+1(x = a0 + ∑jn = 1(ajcos jx + bjsin jx), which may be integrated to provide formulas for either direct quadrature or stepwise integration of differential equations having periodic (or near-periodic) solutions. An “orthogonal” trigonometric sum S2r+1(x) is one that satisfies ∫abS2r+1(x)S2r′+1(x)dx=0, r′
论文关键词:42A52,65D30,42A12,65D05,Trigonometric orthogonality,Gaussian-type quadrature,trigonometric interpolation,numerical integration,differential equations,periodic solutinos
论文评审过程:Available online 20 April 2006.
论文官网地址:https://doi.org/10.1016/0771-050X(76)90045-0