Global errors for approximate approximations with Gaussian kernels on compact intervals
type: Item
instance of: scholarly article
title: Global errors for approximate approximations with Gaussian kernels on compact intervals
zbMATH Open document ID: 1200.41017
author: Zhi-Xiang Chen
author: Feilong Cao
published in: Applied Mathematics and Computation
publication date: 2010-10-25T00:00:00Z
review text: The method of approximate approximations [see \textit{V. Mazýa} and \textit{G. Schmidt}, Approximate approximations. Mathematical Surveys and Monographs. 141. Providence, RI: AMS (2007; Zbl 1120.41013)] is applied to a function defined on a compact interval. After convenient extension of \(f\in C^k[-1,\,1]\) \((k=0,\,1,\,2)\) on \([-1.5,\,1.5]\), \(f\) is approximated by quasi-interpolation on equally spaced nodes with translates of the Gaussian kernel. The authors present error estimates in the uniform norm and this result extend to the corresponding approximation of \(f \in C([-1,\,1]^2)\).
reviewed by: Manfred Tasche
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 41A30
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 5804929
zbMATH Keywords: approximate approximation
zbMATH Keywords: compact interval
zbMATH Keywords: translates of Gaussian kernel
zbMATH Keywords: error estimates
zbMATH Keywords: uniform norm
MaRDI profile type: Publication
full work available at URL: j.amc.2010.06.010
OpenAlex ID: W2059590789
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DOI: 10.1016/J.AMC.2010.06.010
description: scientific article; zbMATH DE number 5804929