Quadratures with multiple nodes, power orthogonality, and moment-preserving spline approximation

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:127

Article

Milovanovic, GV

关键词: quadratures with multiple nodes;    Gauss-Turan-type quadratures;    error term;    convergence;    orthogonal polynomials;    s- and sigma-orthogonal polynomials;    nonnegative measure;    extremal polynomial;    weights;    nodes;    degree of precision;    Stieltjes procedure;    Chebyshev polynomials;    spline function;    spline defect;    moments;   

DOI  :  10.1016/S0377-0427(00)00500-8

来源: Elsevier

【 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 sigma -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. (C) 2001 Elsevier Science B.V. All rights reserved.

【 授权许可】

Free