Multivariate Padé-Bergman approximants
type: Item
instance of: scholarly article
title: Multivariate Padé-Bergman approximants
zbMATH Open document ID: 1018.41010
author: Daniel Boichu
author: Vincent Robin
published in: Numerische Mathematik
publication date: 2003-03-18T00:00:00Z
review text: Slightly modifying a previous definition [\textit{P. Guillaume, A. Huard} and \textit{V. Robin}, J. Approximation Theory 95, 203-214 (1998; Zbl 0916.41015)], the authors define mutivariate Padé-Bergman (or \(A_\rho^2\)) approximants to a function \(f\) on a polydisc via minimizing the Bergman space norm of projections of \(fS-R\) (where \(S\), \(R\) are polynomials) and taking the ratio \(R/S\). This approach simplifies some proofs with respect to the paper cited above. Existence, uniqueness and consistency of these approximants is analyzed. Finally, convergence is studied using tools from both algebraic geometry and complex analysis. In particular, a Montessus de Ballore type theorem is established.
Mathematics Subject Classification ID: 41A21
Mathematics Subject Classification ID: 41A63
Mathematics Subject Classification ID: 65D15
zbMATH DE Number: 1884030
zbMATH Keywords: multivariate Padé approximation
zbMATH Keywords: Bergman spaces
zbMATH Keywords: Montessus de Ballore theorem
reviewed by: Andrei Martínez Finkelshtein
MaRDI profile type: Publication
full work available at URL: s002110200398
OpenAlex ID: W2045466317
DOI: 10.1007/S002110200398
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description: scientific article; zbMATH DE number 1884030