The Optimal Accelerated Overrelaxation Method For Rank Deficient Linear Systems

In this paper, we study the optimal parameters of the AOR iterative method for rank deficient systems by introducing the extrapolation scheme and simplified Mobius transformation. The determination of the two optimal parameters r and w of the AOR iteration matrix is reduced to the optima of extrapolation parameter 9 and the relaxation parameter r of the associated SOR iteration matrix.The development of the classical iterative methods for the solution of linear systems in the last 20th century or more earlier is simply introduced in Chapter 1.In Chapter 2, we give out other subproper AOR splittings for rank deficient linear systems on the base of results which studied by Tian [17]. And some necessary preliminaries of subproper splittings are also introduced.The main results of our paper are in Chapter 3. In this chapter we study the optimal parameters under our conception of optimum by geometry method. The basic properties of extrapolation scheme and Mobius transformation make an important role in our process of obtaining the optimal parameters.