Rational approximation to harmonic functions
type: Item
instance of: scholarly article
title: Rational approximation to harmonic functions
zbMATH Open document ID: 0962.41010
DOI: 10.1023/A:1019172321704
author: Nicholas J. Daras
published in: Numerical Algorithms
publication date: 2001-06-01T00:00:00Z
review text: This is a very nice paper! The author generalizes the concepts of Padé-type and partial Padé-type approximants to the situation of approximating the Fourier series of a harmonic function. The main feature of this type of approximation is the liberty in prescribing poles for the approximating functions. Apart from the usual points of attention (existence, convergence, etc.) there is a section connected with Gaussian quadrature using an interpolating triangle consisting of the zeros of the polynomials orthogonal with respect to the linear functional that generates the rational approximants. The paper concludes with a set of interesting examples.
reviewed by: Marcel G. de Bruin
Mathematics Subject Classification ID: 41A20
Mathematics Subject Classification ID: 30E10
Mathematics Subject Classification ID: 40C05
Mathematics Subject Classification ID: 42A15
zbMATH DE Number: 1355511
zbMATH Keywords: harmonic functions
zbMATH Keywords: Padé-type approximants to Fourier series
zbMATH Keywords: quadrature formulas
MaRDI profile type: Publication
full work available at URL: a:1019172321704
OpenAlex ID: W1861021348
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description: scientific article; zbMATH DE number 1355511