Non-adaptive and adaptive SAOR-CG algorithms

摘要

The paper is concerned with an improvement over the symmetric accelerated overrelaxation (SAOR) method for an iterative solution of large linear systems. At first, the conjugate gradient (CG) acceleration procedure is introduced to the SAOR method, and the non-adaptive SAOR-CG algorithm is developed. Next, the adaptive procedure to determine automatically the CG parameters (νn, ϱn) and the SAOR parameters (γ, ω) is constructed. Based on the adaptive procedure, the adaptive SAOR-CG algorithm is proposed, and its characteristics are shown with numerical experiments. A comparison with the optimum SOR algorithm and the adaptive SSOR algorithm is also given. It is finally proved that the proposed Adaptive SAOR-CG algorithm is feasible and very efficient for the iterative solution.