Toeplitz matrix techniques and convergence of complex weight Padé approximants
type: Item
instance of: scholarly article
title: Toeplitz matrix techniques and convergence of complex weight Padé approximants
zbMATH Open document ID: 0619.41014
DOI: 10.1016/0377-0427(87)90168-3
published in: Journal of Computational and Applied Mathematics
publication date: 1987-01-01T00:00:00Z
review text: One considers diagonal Padé approximants about \(\infty\) of functions of the form \(f(z)=\int^{1}_{-1}(z-x)^{-1}w(x)dx,\) \(z\not\in [-1,1]\), where w is an integrable, possibly complex-valued, function defined on [- 1,1]. Convergence of the sequence of diagonal Padé approximants towards f is established under the condition that there exists a weight \(\omega\), positive almost everywhere on [-1,1], such that \(g(x)=w(x)/\omega (x)\) is continuous and not vanishing on [-1,1]. The rate of decrease of the error is also described. The proof proceeds by establishing the link between the Padé denominators and the orthogonal polynomials related to \(\omega\), in terms of the Toeplitz matrix of symbol g(cos \(\theta)\).
Mathematics Subject Classification ID: 41A29
zbMATH DE Number: 4004841
zbMATH Keywords: diagonal Padé approximants
zbMATH Keywords: Padé denominators
zbMATH Keywords: Toeplitz matrix
author: A. P. Magnus
MaRDI profile type: Publication
full work available at URL: 0377-0427(87)90168-3
OpenAlex ID: W2007272313
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description: scientific article; zbMATH DE number 4004841