Symmetric successive overrelaxation methods for rank deficient linear systems

Abstract

In this paper, we develop symmetric successive overrelaxation (symmetric SOR or SSOR) methods for finding the least square solution of minimal norm to the linear system Ax=b where A is an mxn matrix of rank r. The methods are obtained by first augmenting the system to a block 4x4 consistent system. The augmented coefficient matrix is then split by a subproper SSOR splitting. We state and prove some theorems and by some numerical examples we show the number of iterations for SSOR is less than SOR and accelerated overrelaxation methods for finding the least square solution of minimal norm to the linear system.