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

A parameter-free method, namely the generalization of the Gauss-Seidel (GGS) method, is developed to solve generalized absolute value equations (GAVE). Some results in the recent work of Edalatpour et al. [A generalization of the Gauss-Seidel iteration method for solving absolute value equations. Appl Math Comput. 2017;293:156–167] are extended. For solving linear complementarity problem, the GGS method can be seen as a special case of the accelerated modulus-based matrix splitting iteration method [Zheng and Yin. Accelerated modulus-based matrix splitting iteration methods for linear complementarity problem. Numer Algorithms. 2013;64:245–262], which is characterized by solving a GAVE subproblem in each iteration. Moreover, new convergence results of the GGS method are given. Numerical results demonstrate the effectiveness and efficiency of the GGS method.