Constrained smoothing of histograms by quadratic splines
type: Item
instance of: scholarly article
title: Constrained smoothing of histograms by quadratic splines
zbMATH Open document ID: 0757.65007
DOI: 10.1007/BF02241708
author: Jochen W. Schmidt
published in: Computing
publication date: 1992-09-27T00:00:00Z
review text: Let \(x_ 0<x_ 1<\dots<x_ n\) be fixed points and \(\ell > 0\), \(p_ i > 0\), \(i=1,\dots,n\), be given parameters. The author studies the problem of constructing the quadratic spline \(s(x)\) with knots \(x_ 1,\dots,x_{n-1}\), which minimizes the functional \(K_ q(s):=\ell\| s'\|_{L_ q[x_ 0,x_ n]}+\| p_ i(f_ i-{1\over h_ i}\int^{x_ i}_{x_{i-1}}s(x)dx)\|_{\ell_ q},\) where \(h_ i:=x_ i-x_{i-1}\), \((q=2,\infty)\) under certain constraints like monotonicity, convexity or positivity of \(s\).
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 65D10
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 41A15
zbMATH DE Number: 63397
zbMATH Keywords: histograms
zbMATH Keywords: smoothing
zbMATH Keywords: shape preserving
zbMATH Keywords: constrained approximation
zbMATH Keywords: linear programs
zbMATH Keywords: partially separable programs
zbMATH Keywords: dualization
zbMATH Keywords: Fenchel conjugates
zbMATH Keywords: quadratic spline
zbMATH Keywords: monotonicity
zbMATH Keywords: convexity
zbMATH Keywords: positivity
reviewed by: Borislav D. Bojanov
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02241708
OpenAlex ID: W190163953
description: scientific article; zbMATH DE number 63397