Symmetric successive overrelaxation methods for rank deficient linear systems M.T. Darvishi * , R. Khosro-Aghdam Department of Mathematics, Razi University, Kermanshah 67149, Iran 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 sys- tem Ax = b where A is an m · n matrix of rank r. The methods are obtained by first aug- menting the system to a block 4 · 4 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. Ó 2005 Elsevier Inc. All rights reserved. Keywords: Symmetric successive overrelaxation splitting; Least square solution of minimal norm 1. Introduction Let A be an m · n matrix of rank r P 0 and consider the rectangular system of linear equations 0096-3003/$ - see front matter Ó 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2005.04.090 * Corresponding author. E-mail address: darvishi@razi.ac.ir (M.T. Darvishi). Applied Mathematics and Computation 173 (2006) 404–420 www.elsevier.com/locate/amc