Adapting functions to experimental measurements
type: Item
instance of: scholarly article
title: Adapting functions to experimental measurements
zbMATH Open document ID: 0752.65005
DOI: 10.1016/0898-1221(91)90068-F
author: Lyle Noakes
publication date: 1992-06-26T00:00:00Z
review text: Let \(\phi_ 0: \mathbb{R}\to\mathbb{R}^ 2\) be a given \(C^ \infty\) embedding and \(\phi:\mathbb{R}\to\mathbb{R}^ 2\) be a \(C^ 1\) perturbation of \(\phi_ 0\). The author describes a class of estimation \(\tilde \phi\) for \(\phi_ 0\) defined on the basis of values \(v_ i=\phi(x_ i)\), \(i=1,\dots,n\) and unit normals \(W_ j\) to the curve \(\phi\) at points \(y_ j\), \(j=1,\dots,m\). The measurement \((v_ 1,\dots,v_ n;w_ 1,\dots,w_ m)\) is said to be singular if \(\tilde\phi'(y_ j)\) vanishes for some \(j\). The case of 3 and less points \(y_ j\) is considered in detail and conditions for \(\tilde \phi\) to be singular are analyzed.
Mathematics Subject Classification ID: 65D10
Mathematics Subject Classification ID: 41A25
zbMATH DE Number: 24505
zbMATH Keywords: experimental measurements
zbMATH Keywords: curve sitting
zbMATH Keywords: embedding
zbMATH Keywords: perturbation
zbMATH Keywords: estimators
reviewed by: Borislav D. Bojanov
MaRDI profile type: Publication
cites work: Equivalent Norms for Sobolev Spaces
full work available at URL: 0898-1221(91)90068-f
OpenAlex ID: W2083318918
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 24505