An iterative approach to a constrained least squares problem
type: Item
instance of: scholarly article
title: An iterative approach to a constrained least squares problem
zbMATH Open document ID: 1053.65041
DOI: 10.1155/S1085337503212082
author: Simeon Reich
author: Hong-Kun Xu
published in: Abstract and Applied Analysis
publication date: 2003-06-18T00:00:00Z
full work available at URL: https://eudml.org/doc/51108
review text: Summary: A constrained least squares problem in a Hilbert space \(H\) is considered. The standard Tikhonov regularization method is used. In the case where the set of the constraints is the nonempty intersection of a finite collection of closed convex subsets of \(H\), an iterative algorithm is designed. The resulting sequence is shown to converge strongly to the unique solution of the regularized problem. The net of the solutions to the regularized problems strongly converges to the minimum norm solution of the least squares problem if its solution set is nonempty.
Mathematics Subject Classification ID: 65J10
Mathematics Subject Classification ID: 65J20
Mathematics Subject Classification ID: 47A52
zbMATH DE Number: 1929994
zbMATH Keywords: convergence
zbMATH Keywords: least squares problem
zbMATH Keywords: Hilbert space
zbMATH Keywords: Tikhonov regularization
zbMATH Keywords: iterative algorithm
zbMATH Keywords: minimum norm solution
MaRDI profile type: Publication
OpenAlex ID: W2067538198
description: scientific article; zbMATH DE number 1929994