On orthogonal linear \(\ell_1\) approximation
type: Item
instance of: scholarly article
title: On orthogonal linear \(\ell_1\) approximation
zbMATH Open document ID: 0633.65010
DOI: 10.1007/BF01400354
author: Helmuth Späth
author: G. A. Watson
published in: Numerische Mathematik
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133211
review text: By using a special approach to a given data fitting problem the authors arrive at a minimization problem of the following form: minimize \(\| Zv\|_ 1\) subject to \(v\in {\mathbb{R}}^ n\) and \(\| v\|_ 2=1\), where Z is a given \(m\times n\)-matrix. This problem is equivalent to a concave quadratic programming problem. A characterization of local solutions and a result on the stability of these solutions under small perturbations of the matrix Z is given. Moreover, an algorithm for solving the minimization problem is presentd and its convergence to a special solution is shown. Finally, the performance of the algorithm is illustrated by applying the method to some examples known in the literature.
Mathematics Subject Classification ID: 65D10
Mathematics Subject Classification ID: 41A50
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C20
zbMATH DE Number: 4030807
zbMATH Keywords: orthogonal \(\ell _ 1\)-fitting
zbMATH Keywords: orthogonal \(\ell _ 1\)-approximation
zbMATH Keywords: algorithm
zbMATH Keywords: data fitting
zbMATH Keywords: minimization problem
zbMATH Keywords: concave quadratic programming problem
zbMATH Keywords: local solutions
zbMATH Keywords: stability
zbMATH Keywords: convergence
MaRDI profile type: Publication
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OpenAlex ID: W2064346177
description: scientific article; zbMATH DE number 4030807