A generalization of the Gauss-Seidel iteration method for solving absolute value equations

Based on the Gauss-Seidel splitting, we present a new matrix splitting iteration method, called generalized Gauss-Seidel (GGS) iteration method, for solving the large sparse absolute value equation (AVE) Ax - vertical bar x vertical bar = b where A is an element of R-nxn and b is an element of R-n and investigate its convergence properties. Moreover, by preconditioning AVE, a preconditioned variant of the GGS (PGGS) method is presented. Numerical experiments illustrate the efficiency of both GGS and PGGS iterations. (C) 2016 Elsevier Inc. All rights reserved.