Padé and Padé-type approximation for \(2\pi\)-periodic \(L^p\) functions
type: Item
instance of: scholarly article
title: Padé and Padé-type approximation for \(2\pi\)-periodic \(L^p\) functions
zbMATH Open document ID: 0976.41017
DOI: 10.1023/A:1006459830925
author: Nicholas J. Daras
published in: Acta Applicandae Mathematicae
publication date: 2001-12-28T00:00:00Z
review text: The main contribution of the paper is the introduction of the notion of composed Padé-type approximants. That are Padé-type approximants for complex functions where the generating polynomial for the real and the imaginary part of the function can be different. Definition and convergence properties are addressed. This is subsequently applied to harmonic functions and \(L^p\) functions. Numerical examples and two applications are mentioned (acceleration of convergence and approximate computation of derivatives and integrals). Many results of the paper are formulated not just for Padé or Padé-type approximation, but are formulated in a more general context of rational interpolation (with prescribed poles). The paper has also a relatively long historical introduction on rational approximation and continued fractions.
reviewed by: Adhemar Bultheel
Mathematics Subject Classification ID: 41A21
Mathematics Subject Classification ID: 42A10
Mathematics Subject Classification ID: 30E10
Mathematics Subject Classification ID: 40C05
zbMATH DE Number: 1563267
zbMATH Keywords: Padé approximation
zbMATH Keywords: Padé-type approximation
zbMATH Keywords: rational interpolation
zbMATH Keywords: Poisson integral
MaRDI profile type: Publication
full work available at URL: a:1006459830925
OpenAlex ID: W2915010830
description: scientific article; zbMATH DE number 1563267