The \(L_p\)-approximation order of surface spline interpolation for \(1\leq p\leq 2\)
type: Item
instance of: scholarly article
title: The \(L_p\)-approximation order of surface spline interpolation for \(1\leq p\leq 2\)
zbMATH Open document ID: 1062.41004
author: Michael J. Johnson
published in: Constructive Approximation
publication date: 2004-10-28T00:00:00Z
review text: The author studies the problem of \(L_p-\) approximation order of surface spline interpolation. In [Constructive Approximation 14, No.3, 429-438 (1998; Zbl 0904.41005)] and [Math.Comp. 70, No.234, 719-737 (2001; Zbl 0973.41005)] respectively, the author obtained upper and lower bounds for the \(L_p-\) approximation order of surface spline interpolation. It is shown here that the \(L_p-\) approximation order of surface spline interpolation equals \(m+\frac {1}{p}\) for \(1\leq p \leq 2\), where \(m\) is an integer parameter which specifies the surface spline. The author also states numerical evidence to support the conjecture that the \(L_p-\) approximation order of surface spline interpolation is \(m+\frac {1}{p}\) for \(2<p \leq \infty\) also.
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 65D05
zbMATH DE Number: 2111560
zbMATH Keywords: interpolation
zbMATH Keywords: surface spline
zbMATH Keywords: approximation order
reviewed by: H. P. Dikshit
MaRDI profile type: Publication
full work available at URL: s00365-003-0534-5
OpenAlex ID: W2000694913
DOI: 10.1007/S00365-003-0534-5
description: scientific article; zbMATH DE number 2111560