On the convergence of periodic splines of arbitrary degree
type: Item
instance of: scholarly article
title: On the convergence of periodic splines of arbitrary degree
zbMATH Open document ID: 0691.41012
DOI: 10.1016/0021-9045(88)90068-8
author: Franz-Jürgen Delvos
published in: Journal of Approximation Theory
publication date: 1988-01-01T00:00:00Z
review text: The author considers an interpolation problem with 1-periodic polynomial splines of degree m with spline knots i/n (i\(\in {\mathbb{Z}}\); \(n>1)\). A new error estimate the following type is proved under the assumption that there exists a unique spline interpolation an arbitrary given 1-periodic function at the interpolation points (i-\(\lambda)\)/n (i\(\in {\mathbb{Z}}\); \(0\leq \lambda <1):\) If s is the 1-periodic spline interpolant of a given 1-periodic function \(f\in C^{m+1}({\mathbb{R}})\), then \(\| f^{(k)}- s^{(k)}\|_{\infty}=O(n^{-m-1+k})\) (0\(\leq k\leq m)\). This generalizes special results of \textit{F. Dubeau} and \textit{J. Savoie} [J. Approximation Theory 39, 77-88 (1983; Zbl 0516.41005) and IMA J. Numer. Anal. 5, 183-189 (1985; Zbl 0566.41029)]. Using the discrete Fourier transform and cyclic convolution, a numerical procedure is described.
reviewed by: Manfred Tasche
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 65D07
zbMATH DE Number: 4130939
zbMATH Keywords: polynomial splines
zbMATH Keywords: error estimate
zbMATH Keywords: discrete Fourier transform
zbMATH Keywords: cyclic convolution
zbMATH Keywords: numerical procedure
MaRDI profile type: Publication
full work available at URL: 0021-9045(88)90068-8
OpenAlex ID: W2027805326
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description: scientific article; zbMATH DE number 4130939