Abstract and Applied Analysis
Volume 2003 (2003), Issue 7, Pages 387-406
doi:10.1155/S108533750321201X

Iterative algorithms with seminorm-induced oblique projections

Yair Censor1 and Tommy Elfving2

1Department of Mathematics, University of Haifa, Mt. Carmel, Haifa 31905, Israel
2Mathematics Department, Linköping University, Linköping SE-581 83, Sweden

Received 29 October 2001; Revised 23 September 2002

Copyright © 2003 Yair Censor and Tommy Elfving. 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.

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.