On the quality of algorithms based on spline interpolation
type: Item
instance of: scholarly article
title: On the quality of algorithms based on spline interpolation
zbMATH Open document ID: 0872.65006
DOI: 10.1007/BF02207693
author: Helmut Brass
published in: Numerical Algorithms
publication date: 1997-10-19T00:00:00Z
review text: Let \(C^*\) denote the space of real valued \(n\)-periodic continuous functions endowed with the sup-norm, and let \(I\) be a continuous linear functional on \(C^*\). The paper is devoted to the approximate computation of \(I[f]\) using as input only the function values \(f(j)\), \(j=1, \dots,n\), and the supplementary information \(|f^{(r)}|\leq 1\), where \(r\) is fixed. The quality \(q\) of a numerical algorithm for the computation of \(I[f]\) is defined as the ratio of its error to the smallest possible error of an algorithm based on the same information. It is shown that \(q\) is rather small if the algorithm is based on periodic spline interpolation.
reviewed by: Johannes Elschner
Mathematics Subject Classification ID: 65D15
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 65D07
zbMATH DE Number: 993903
zbMATH Keywords: optimal algorithm
zbMATH Keywords: information based complexity
zbMATH Keywords: continuous linear functional
zbMATH Keywords: periodic spline interpolation
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 993903