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−|x|=bAx−|x|=b where A∈Rn×nA∈Rn×n and b∈Rnb∈Rn 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.