Abstract and Applied Analysis

Abstract and Applied Analysis / 2003 / Article

Open Access

Volume 2003 |Article ID 673252 | https://doi.org/10.1155/S108533750321201X

Yair Censor, Tommy Elfving, "Iterative algorithms with seminorm-induced oblique projections", Abstract and Applied Analysis, vol. 2003, Article ID 673252, 20 pages, 2003. https://doi.org/10.1155/S108533750321201X

Iterative algorithms with seminorm-induced oblique projections

Received29 Oct 2001
Revised23 Sep 2002

Abstract

A definition of oblique projections onto closed convex sets that use seminorms induced by diagonal matrices which may have zeros on the diagonal is introduced. Existence and uniqueness of such projections are secured via directional affinity of the sets with respect to the diagonal matrices involved. A block-iterative algorithmic scheme for solving the convex feasibility problem, employing seminorm-induced oblique projections, is constructed and its convergence for the consistent case is established. The fully simultaneous algorithm converges also in the inconsistent case to the minimum of a certain proximity function.

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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