Quadratures with multiple nodes, power orthogonality, and moment-preserving spline approximation
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摘要
Quadrature formulas with multiple nodes, power orthogonality, and some applications of such quadratures to moment-preserving approximation by defective splines are considered. An account on power orthogonality (s- and σ-orthogonal polynomials) and generalized Gaussian quadratures with multiple nodes, including stable algorithms for numerical construction of the corresponding polynomials and Cotes numbers, are given. In particular, the important case of Chebyshev weight is analyzed. Finally, some applications in moment-preserving approximation of functions by defective splines are discussed.
论文关键词：Quadratures with multiple nodes,Gauss–Turán-type quadratures,Error term,Convergence,Orthogonal polynomials,s- and σ-orthogonal polynomials,Nonnegative measure,Extremal polynomial,Weights,Nodes,Degree of precision,Stieltjes procedure,Chebyshev polynomials,Spline function,Spline defect,Moments
论文评审过程：Received 29 October 1999, Available online 12 January 2001.
论文官网地址：https://doi.org/10.1016/S0377-0427(00)00500-8
