Optimal error bounds for Hermite interpolation
type: Item
instance of: scholarly article
title: Optimal error bounds for Hermite interpolation
zbMATH Open document ID: 0636.41002
DOI: 10.1016/0021-9045(87)90043-8
author: A. K. Varma
author: K. L. Katsifarakis
published in: Journal of Approximation Theory
publication date: 1987-01-01T00:00:00Z
review text: Let \(u(x)\in C^ 3[0,1]\) and \(v_ 3(x)\) the unique Hermitian interpolation polynomial of degree \(\leq 3\) satisfying \(v_ 3(0)=u(0)\), \(v_ 3(1)=u(1)\), \(v_ 3'(0)=u'(0)\), \(v_ 3'(1)=u'(1)\). The authors obtain pointwise bounds for the error \(e(x)=v_ 3(x)-u(x)\) and its derivatives in terms of \(L=\max (| u\prime''(x)|;\quad 0\leq x\leq 1)\) or in terms of \(M=\max (| u''(x)|\); \(0\leq x\leq 1)\). These estimates complete those obtained by \textit{P. G. Ciarlet}, \textit{M. H. Schultz}, \textit{R. S. Varga} [Numer. Math. 9, 394-430 (1967; Zbl 0155.204)] and \textit{G. Birkhoff}, \textit{A. Priver} [J. Math. Phys. 46, 440-447 (1967; Zbl 0176.142)]. In addition, these estimates are the best possible.
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A10
zbMATH DE Number: 4036359
zbMATH Keywords: Hermitian interpolation polynomial
reviewed by: Radu Precup
MaRDI profile type: Publication
full work available at URL: 0021-9045(87)90043-8
OpenAlex ID: W2048295521
cites work: Hermite Interpolation Errors for Derivatives
cites work: Numerical methods of high-order accuracy for nonlinear boundary value problems. I: One dimensional problem
cites work: Q3848301
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description: scientific article; zbMATH DE number 4036359