On the convergence of the SAOR method and the error bounds for its acceleration

摘要

Given a linear system with Hermitian positive definite coefficient matrix A, a splitting of Varga's type [1] is considered, and the corresponding generalised SAOR scheme is presented. We obtain the convergence theorem for the SAOR method and give the error bound for the A-norm of the error vector for the SAOR semi-iterative method, hence extending the SAOR theory.