SYMMETRICAL MULTISPLITTING OF A SYMMETRICAL POSITIVE-DEFINITE MATRIX

A parallel symmetric multisplitting method for solving a symmetric pos itive system Ax = b is presented. Here the s.p.d. (symmetric positive definite) matrix A need not be assumed in a special form (e.g. the dis section form (R.E. White, SIAM J. Matrix Anal. Appl. 11 (1990) 69-82). The main tool for deriving our method is the diagonally compensated r eduction (cf. (O. Axelsson, L. Kolotilina, Numer. Linear Algebra Appl. 1 (1994) 155-177)). The convergence of the presented parallel symmetr ic multisplitting method is also discussed by using this tool. (C) 199 8 Elsevier Science Inc. All rights reserved.