Contrained interpolants with minimal \(W^{k,p}\)-norm
type: Item
instance of: scholarly article
title: Contrained interpolants with minimal \(W^{k,p}\)-norm
zbMATH Open document ID: 0607.41012
DOI: 10.1016/0021-9045(87)90105-5
author: L.-E. Andersson
author: Per-Anders Ivert
published in: Journal of Approximation Theory
publication date: 1987-01-01T00:00:00Z
review text: The problem of minimizing \(\| f^{(k)}\|_ p\) \((1<p<\infty)\) under the constraints \(f^{(k)}(t)\geq 0\) and \(f^{(k)}(t_ i)=y_ i\) for given points \((t_ i,y_ i)\), \(i=1,2,...,N+k\), with positive kth divided difference is considered. It is shown that f solves this problem if and only if \[ f^{(k)}(t)=(\sum^{N}_{i=1}\alpha_ iM_{i,k}(t))_+^{1/(p-1)} \] where \(\alpha_ 1,...,\alpha_ N\) are real numbers and the \(M_{i,k}\) are basic spline functions.
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A29
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 49K30
zbMATH DE Number: 3981740
zbMATH Keywords: interpolating splines
zbMATH Keywords: constraints
zbMATH Keywords: divided difference
MaRDI profile type: Publication
full work available at URL: 0021-9045(87)90105-5
OpenAlex ID: W1978963914
cites work: Sur l'interpolation
cites work: Interpolation by smooth functions under restrictions on the derivatives
cites work: Q3217070
description: scientific article; zbMATH DE number 3981740