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13 April 2003 Iterative algorithms with seminorm-induced oblique projections
Yair Censor, Tommy Elfving
Abstr. Appl. Anal. 2003(7): 387-406 (13 April 2003). DOI: 10.1155/S108533750321201X


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.


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Yair Censor. Tommy Elfving. "Iterative algorithms with seminorm-induced oblique projections." Abstr. Appl. Anal. 2003 (7) 387 - 406, 13 April 2003.


Published: 13 April 2003
First available in Project Euclid: 15 April 2003

zbMATH: 1047.90042
MathSciNet: MR1982660
Digital Object Identifier: 10.1155/S108533750321201X

Primary: 49M20 , 90C25
Secondary: 65K05

Rights: Copyright © 2003 Hindawi

Vol.2003 • No. 7 • 13 April 2003
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