On certain symmetric strong distributions, two-point Padé approximation and related quadratures

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• 作者：C. D&#xed ; az-Mendoza ; P. Gonz&#xe1 ; lez-Vera ; M. Jim&#xe9 ; nez Paiz ; R. Orive
• 关键词：Two-point Pad&#xe9 ; -type approximation ; Strong distributions ; Cauchy transform ; Orthogonal polynomials
• 刊名：Applied Numerical Mathematics
• 出版年：2009
• 出版时间：August 2009
• 年：2009
• 卷：59
• 期：8
• 页码：2002-2014
• 全文大小：252 K

文摘

Let be a c-inversive strong distribution as defined in [A. Sri Ranga, E.X.L. de Andrade, J.H. McCabe, Some consequences of a symmetry in strong distributions, J. Math. Anal. Appl. 193 (1) (1995) 158–168]. In this paper, two-point Padé approximants, both with free and prescribed poles, related to the distribution are analyzed. In particular, the existence of c-inversive rational approximants to the Stieltjes transform of is studied, in order to make computations in an advantageous way. An application to numerical quadratures is also given, and several examples applying these Gauss-type quadrature formulas in the case of integrands which can be well approximated by Laurent polynomials are displayed, showing better results than the corresponding for the usual Gaussian rules.