From numerical quadrature to Pade approximation

被引：7
作者：
Brezinski, C. [1 ]
机构：
[1] Univ Sci & Technol Lille, CNRS, Lab Paul Painleve, UFR Math Pures & Appliquees,UMR 8524, F-59655 Villeneuve Dascq, France
来源：
APPLIED NUMERICAL MATHEMATICS | 2010年 / 60卷 / 12期
关键词：
Pade approximantion; Quadrature; Convergence acceleration; Extrapolation; ORTHOGONAL POLYNOMIALS; GAUSS QUADRATURE; CLENSHAW-CURTIS; ERROR; FORMULAS;
D O I：
10.1016/j.apnum.2010.06.001
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The paper reviews the relation between Pade-type approximants of a power series and interpolatory quadrature formulae with free nodes, and between Pade approximants and Gaussian quadrature methods. Then, it is shown how the Kronrod procedure and the anti-Gaussian quadrature methods could be used for estimating the error in Pade approximation. The epsilon-algorithm for accelerating the convergence of sequences, and computing recursively Parte approximants is evoked, and its error estimated by the same procedures. Finally, the case of series of functions is considered. Considerations on further research topics end the paper. (C) 2010 IMACS. Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：1209 / 1220
页数：12
相关论文
共 39 条
[1]  
BAILLAUD R, 1905, CORRES HERMITE STIEL
[2]  
Baker George A., 1996, Pade Approximants, V59
[3]   ERROR ESTIMATE IN VECTOR PADE-APPROXIMATION [J].
BELANTARI, A .
APPLIED NUMERICAL MATHEMATICS, 1991, 8 (06) :457-468
[4]  
BELANTARI A, 1989, THESIS U SCI TECHNOL
[5]   Anti-Gaussian Pade approximants [J].
Boutry, G .
NUMERICAL ALGORITHMS, 2003, 33 (1-4) :113-122
[6]   DUALITY IN PADE-TYPE APPROXIMATION [J].
BREZINSKI, C .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1990, 30 (03) :351-357
[7]   Error estimates for the solution of linear systems [J].
Brezinski, C .
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1999, 21 (02) :764-781
[8]  
Brezinski C., 1975, Calcolo, V12, P317, DOI 10.1007/BF02575753
[9]   Quasi-orthogonality with applications to some families of classical orthogonal polynomials [J].
Brezinski, C ;
Driver, KA ;
Redivo-Zaglia, M .
APPLIED NUMERICAL MATHEMATICS, 2004, 48 (02) :157-168
[10]   Krylov subspace methods, biorthogonal polynomials and Pade-type approximants [J].
Brezinski, C .
NUMERICAL ALGORITHMS, 1999, 21 (1-4) :97-107
1234