Notes on some estimations in rational approximation. I
type: Item
instance of: scholarly article
title: Notes on some estimations in rational approximation. I
zbMATH Open document ID: 0654.41015
DOI: 10.1007/BF01848003
author: S. H. Smith
published in: Periodica Mathematica Hungarica
publication date: 1988-01-01T00:00:00Z
review text: Several problems in rational approximation are discussed. For instance, an asymptotic expansion is given for \(S_ n=\max | R_ n(x)-e^{- x}|,\) where the maximum is taken over \([0,\infty)\), and \(R_ n(x)=1/\sum^{n}_{k=0}x^ k/k!\) An earlier result \(s_ n<2^{-n}\) is replaced by a sharper estimate. Also, approximations to \((1- x)^{\alpha}\) are considered and Laguerre-Padé approximants. The paper shows an interesting combination of asymptotic and numerical approximations.
Mathematics Subject Classification ID: 41A20
Mathematics Subject Classification ID: 41A60
zbMATH DE Number: 4067517
zbMATH Keywords: Laguerre-Padé approximants
zbMATH Keywords: numerical approximations
reviewed by: Nico M. Temme
MaRDI profile type: Publication
cites work: Chebyshev rational approximations to \(e^{-x}\) in \([0,+\infty)\) and applications to heat-conduction problems
cites work: Q5824493
cites work: Problems and results in rational approximation
cites work: A note on rational approximation to \((1-x)^{\alpha}\)
cites work: Laguerre Functions in the Mathematical Foundations of the Electromagnetic Theory of the Paraboloidal Reflector
description: scientific article; zbMATH DE number 4067517