Semiconvergence of parallel multisplitting methods for symmetric positive semidefinite linear systems

Abstract

In this paper we construct some parallel relaxed multisplitting methods for solving consistent symmetric positive semidefinite linear systems, based on modified diagonally compensated reduction and incomplete factorizations. The semiconvergence of the parallel multisplitting method, relaxed multisplitting method and relaxed two-stage multisplitting method are discussed. The results generalize some well-known results for the nonsingular linear systems to the singular systems.