Symmetric multisplitting of a symmetric positive definite matrix Original Research Article

A parallel symmetric multisplitting method for solving a symmetric positive 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 dissection form (R.E. White, SIAM J. Matrix Anal. Appl. 11 (1990) 69–82). The main tool for deriving our method is the diagonally compensated reduction (cf. (O. Axelsson, L. Kolotilina, Numer. Linear Algebra Appl. 1 (1994) 155–177)). The convergence of the presented parallel symmetric multisplitting method is also discussed by using this tool.