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
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.