Iterative algorithms with seminorm-induced oblique projections

Yair Censor, Tommy Elfving

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)387-406
Number of pages20
JournalAbstract and Applied Analysis
Issue number7
StatePublished - 13 Apr 2003

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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