Iterative algorithms with seminorm-induced oblique projections. (13th April 2003)

• Record Type: Journal Article
• Authors: Censor, Yair; Elfving, Tommy
• Is Part Of: Abstract and applied analysis. Volume 2003:Number 7(2003)
• Page Start: 387
• Page End: 406
• Publication Date: 2003-04-13
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/S108533750321201X
• Languages: English
• ISSNs: 1085-3375

Abstract

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.