Convergence of Lagrange Interpolation Polynomials for Piecewise Smooth Functions

S. Zhou; L. Zhu

doi:10.1023/a:1013817432519

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Acta Mathematica Hungarica

Volume/Issue:: Volume 93: Issue 1-2

Convergence of Lagrange Interpolation Polynomials for Piecewise Smooth Functions

Authors:

S. Zhou

S. Zhou Ningbo University The Mathematical Institute Ningbo, Zhejiang 315211 China e-mail Ningbo, Zhejiang 315211 China e-mail

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and

L. Zhu

L. Zhu People's University of China Department of Information Beijing 100872 China Beijing 100872 China

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Pages:: 71–76

Online Publication Date:: 03 Nov 2004

Publication Date:: 01 Oct 2001

Article Category:: Research Article

DOI:: https://doi.org/10.1023/a:1013817432519

Keywords:: Lagrange interpolation; piecewise smooth functions

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Abstract

The present paper first establishes a decomposition result for f(x)∈ C^rC^r+1. By using this decomposition we thus can obtain an estimate of ∣f(x) - L_n(f,x)∣ which reflects the influence of the position of the x's and ω(f^(r+1),δ)_j, j = 0,1,...,s, on the error of approximation.

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Acta Mathematica Hungarica

Print ISSN:: 0236-5294

Online ISSN:: 1588-2632

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Acta Mathematica Hungarica
Language	English
Size	B5
Year of Foundation	1950
Volumes per Year	3
Issues per Year	6
Founder	Magyar Tudományos Akadémia
Founder's Address	H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher	Akadémiai Kiadó Springer Nature Switzerland AG
Publisher's Address	H-1117 Budapest, Hungary 1516 Budapest, PO Box 245. CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible Publisher	Chief Executive Officer, Akadémiai Kiadó
ISSN	0236-5294 (Print)
ISSN	1588-2632 (Online)