A piecewise polynomial lacunary interpolation method
type: Item
instance of: scholarly article
title: A piecewise polynomial lacunary interpolation method
zbMATH Open document ID: 0631.41004
DOI: 10.1016/0021-9045(86)90012-2
author: Th. Fawzy
author: Larry L. Schumaker
published in: Journal of Approximation Theory
publication date: 1986-01-01T00:00:00Z
review text: The following general lacunary interpolation problem is solved: let \(\Delta =\{x_ 1<x_ 2<...<x_{n+1}\}\) and let \(\nu_ 1,...,\nu_ p\) be integers with \(0\leq \nu_ 1<...<\nu_ p\). Suppose \(\{f_ i^{\nu_ j}\}\), \(j=1,...,p\); \(i=1,...,n+1\) are given real numbers. Find a function f defined on \([x_ 1,x_{n+1}]\) such that \(D^{\nu_ j}f(x_ i)=f_ i^{\nu_ j}\), \(j=1,...,p\) and \(i=1,...,n+1\). Special piecewise polynomial methods are developed for the solution. It is further shown that for typical smooth classes of functions the methods deliver optimal-order approximations.
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 41A25
zbMATH DE Number: 4026036
zbMATH Keywords: lacunary interpolation
zbMATH Keywords: piecewise polynomial methods
zbMATH Keywords: optimal-order approximations
MaRDI profile type: Publication
full work available at URL: 0021-9045(86)90012-2
OpenAlex ID: W2011624610
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description: scientific article; zbMATH DE number 4026036