Notes on lacunary interpolation with splines IV. (0,2) interpolation with splines of degree 6
type: Item
instance of: scholarly article
title: Notes on lacunary interpolation with splines IV. (0,2) interpolation with splines of degree 6
zbMATH Open document ID: 0659.41012
DOI: 10.1016/0021-9045(87)90081-5
author: F. Holail
author: Th. Fawzy
published in: Journal of Approximation Theory
publication date: 1987-01-01T00:00:00Z
review text: The authors study the following (0,2)-interpolation problem: Given \(\Delta =\{x_ i\}^ n_{i=0}\), \(x_ i=ih\) and the real numbers \(\{f_ i,f_ i''\}^ n_{i=0}\), find S such that \(S(x_ i)=f_ i\), \(S''(x_ i)=f_ i''\), \(i=0,1,...,n\). Using piecewise polynomials of degree 6, they construct a solution S of this problem and show that: if \(f\in C^ 6[0,1]\), then \(| f^{(j)}(x)-S^{(j)}(x)| \leq C^*_{kj}h^{6-j}\omega (f^{(6)};h),\) for \(x_ k\leq x\leq x_{k+1}\), \(0\leq k\leq n-1\), \(0\leq j\leq 6\), where \(C^*_{kj}\) are effectively calculated.
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A05
zbMATH DE Number: 4077932
zbMATH Keywords: (0,2)-interpolation problem
reviewed by: Radu Precup
MaRDI profile type: Publication
full work available at URL: 0021-9045(87)90081-5
OpenAlex ID: W2047350266
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description: scientific article; zbMATH DE number 4077932