Abstract and Applied Analysis

Abstract and Applied Analysis / 2003 / Article

Open Access

Volume 2003 |Article ID 104964 | https://doi.org/10.1155/S1085337503212082

Simeon Reich, Hong-Kun Xu, "An iterative approach to a constrained least squares problem", Abstract and Applied Analysis, vol. 2003, Article ID 104964, 10 pages, 2003. https://doi.org/10.1155/S1085337503212082

An iterative approach to a constrained least squares problem

Received03 Dec 2001

Abstract

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.

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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