Accelerated Successive Overrelaxation (ASOR) Method

The augmented system of linear equations has appeared in different ap-plications of scientific computing including, weighted least-squares problems, fi-nite element discretization of the Navier-Stokes equations, constrained optimiza-tion, equilibrium system and saddle point problems. In the paper about succesive overrelaxation-like (SOR-like) method for augmented systems, Golub, Wu and Yuan (2001) presented several SOR-like algorithms to solve augmented systems. By ac-celerating SOR-like method with two parameters a and w, we propose accelerated SOR-like (ASOR) method for augmented systems.In this paper, we have presented four chapters. In Chapter 1, we discuss it-erative methods for augmented linear systems. We have focused on the classical methods as well as different modified SOR methods. In Chapter 2, we review some of the existing methods for solving the augmented linear systems as our background, we have also given an outline of SOR-like method and preconditioned conjugate gra-dient (PCG) method. In Chapter 3, the outline of ASOR method is discussed with a new splitting of the augmented system. Basic relation involving a and w, eigen-values of ASOR method and matrix Q-1BTA-1B and analysis of the convergence of ASOR method are discussed under suitable restrictions on iterative parameters. In Chapter 4, Some numerical examples and results are presented to show the ef-ficiency of ASOR method with a suitable choice of the parameters a and w. We have compared ASOR method with SOR-like method (Golub, Wu and Yuan,2001), GSOR method (Bai, Parlett and Wang,2005) and GSSOR method (Chao, Zhang and Lu,2014) in order to demonstrate its efficiency and superiority.