Histospline projections on a uniform partition
type: Item
instance of: scholarly article
title: Histospline projections on a uniform partition
zbMATH Open document ID: 0663.41013
DOI: 10.1016/0021-9045(88)90107-4
author: F. Dubeau
author: Jean Savoie
published in: Journal of Approximation Theory
publication date: 1988-01-01T00:00:00Z
review text: Let \(x_ i=a+ih\), \(i=0,...,N\), \(h=(b-a)/N\) be a uniform partition of the interval [a,b]. The paper is concerned with the existence and unicity of periodic histospline projections s determined by the conditions \(\int_{\Delta_ i}s(x)dx=\int_{\Delta_ i}f(c)dx\), \(\Delta_ i=[x_ i+vh,\quad x_ i+(v+1)h]\), \(i=0,...,N-1\), where \(v\in [0,1]\) is fixed and f is a function with continuous and periodic derivatives up to order \(n+1\) on [a,b]. The proofs are based on a linear dependence formula relating the quantities \(s^{(k)}(x_ i+uh)\) and the integrals of s over \([x_ i+vh\), \(x_ i+(v+l)h]\), \(u,v\in [0,1]\), proved by the authors in an earlier paper [Ann. Sci. Math. Que. 10, 5-15 (1986)]. Error bounds of the form \(\| f^{(k)}-s^{(k)}\|_{\infty}\simeq O(h^{n+1-k})\) are also obtained.
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A65
zbMATH DE Number: 4084249
zbMATH Keywords: periodic histospline projections
zbMATH Keywords: Error bounds
reviewed by: Stefan Cobzaş
MaRDI profile type: Publication
full work available at URL: 0021-9045(88)90107-4
OpenAlex ID: W2006230478
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description: scientific article; zbMATH DE number 4084249