Quadrature and orthogonal rational functions

被引：20
|
作者：
Bultheel, A
González-Vera, P
Hendriksen, E
Njåstad, O
机构：
[1] Katholieke Univ Leuven, Dept Comp Sci, B-3001 Louvain, Belgium
[2] Univ La Laguna, Dept Anal, Tenerife, Spain
[3] Univ Amsterdam, Dept Math, Amsterdam, Netherlands
[4] Norwegian Univ Sci & Technol, Dept Math Sc, N-7034 Trondheim, Norway
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2001年 / 127卷 / 1-2期
关键词：
numerical quadrature; orthogonal rational functions; multipoint Pade approximation;
D O I：
10.1016/S0377-0427(00)00493-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Classical interpolatory or Gaussian quadrature formulas are exact on sets of polynomials. The Szego quadrature formulas are the analogs for quadrature on the complex unit circle. Here the formulas are exact on sets of Laurent polynomials. In this payer we consider generalizations of these ideas, where the (Laurent) polynomials are replaced by rational functions that have prescribed poles, These quadrature formulas are closely related to certain multipoint rational approximants of Cauchy or Riesz-Herglotz transforms of a (positive or general complex) measure. We consider the construction and properties of these approximants and the corresponding quadrature formulas as well as the convergence and rate of convergence. (C) 2001 Elsevier Science B.V. All rights reserved. MSC: 65D30; 33D45; 41A21.
引用
收藏
页码：67 / 91
页数：25
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