A class of parallel decomposition-type relaxation methods for large sparse systems of linear equations

A class of parallel decomposition-type accelerated over-relaxation methods, including four arbitrary parameters and suitable to the SIMD-systems, is established for solving the large sparse systems of linear equations in this paper, and sufficient conditions ensuring its convergence are deduced when the coefficient matrices of the linear systems of equations are respectively L-matrices, H-matrices and positive definite matrices. In particular, we investigate in detail the symmetric versions of these new methods, and deduce a series of conveniently applicable conditions for determining the convergence of these versions when the coefficient matrices of the linear systems of equations are symmetric positive definite matrices. (C) 1998 Elsevier Science Inc. All rights reserved.