Title: Quadrature and orthogonal rational functions
Authors: Bultheel, Adhemar ×
González-Vera, Pablo
Hendriksen, Erik
Njåstad, Olav #
Issue Date: Jan-2001
Publisher: Elsevier science bv
Series Title: Journal of computational and applied mathematics vol:127 issue:1-2 pages:67-91
Abstract: 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.
ISSN: 0377-0427
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

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