Spline fitting discontinuous functions given just a few Fourier coefficients
type: Item
instance of: scholarly article
title: Spline fitting discontinuous functions given just a few Fourier coefficients
zbMATH Open document ID: 0827.65012
DOI: 10.1007/BF02143932
author: R. K. Wright
published in: Numerical Algorithms
publication date: 1995-12-11T00:00:00Z
review text: Let \(f\) be a given \(p\)-periodic, piecewise \(C^1\)-function. The author uses \(p\)-periodic (quadratic) splines with equidistant nodes to approximate \(f\) when few Fourier coefficients of \(f\) and the locations of the jump discontinuities of \(f\) and \(f'\) are known. It is assumed that the locations of these discontinuities are special spline nodes. The results deal with the orthogonal projection \(P\) of the considered spline space onto the space of trigonometric polynomials. The reconstruction of \(f\) is based on inverting \(P\). It is shown that \(P\) is invertible and its inverse has a normal close to 1. A numerical example is given.
reviewed by: Manfred Tasche
Mathematics Subject Classification ID: 65D10
Mathematics Subject Classification ID: 65T40
zbMATH DE Number: 770302
zbMATH Keywords: discontinuous functions
zbMATH Keywords: inversion of Fourier expansion
zbMATH Keywords: spline fitting
zbMATH Keywords: periodic (quadratic) splines
zbMATH Keywords: trigonometric polynomials
zbMATH Keywords: reconstruction
describes a project that uses: SEGMENTD
describes a project that uses: Maple
MaRDI profile type: Publication
cites work: Attenuation factors in practical Fourier analysis
cites work: Q4002478
cites work: Q3895980
cites work: Q3779677
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description: scientific article; zbMATH DE number 770302