PARALLEL, SYNCHRONOUS AND ASYNCHRONOUS TWO-STAGE MULTISPLITTING METHODS
Rafael Bru, Violeta Migallón, José Penadés, Daniel B. Szyld · 1995
. Di#erent types of synchronous and asynchronous two-stage multisplitting algorithms for the solution of linear systems are analyzed. The di#erent algorithms which appeared in the literature are reviewed, and new ones are presented. Convergence properties of these algorithms are studied when the matrix in question is either monotone or an H-matrix. Relaxed versions of these algorithms are also studied. Computational experiments on a shared memory multiprocessor vector computer are presented. Key words. asynchronous methods, two-stage iterative methods, linear systems, multisplittings, parallel algorithms. AMS subject classifications. 65F10, 65F15. 1. Introduction. In this paper we present various types of synchronous and asynchronous two-stage multisplitting algorithms for the solution of linear systems of the form Ax = b, (1.1) where A is an n n nonsingular matrix. We first give a general convergence result, and then, for the most part, concentrate our study on two important cases...