SHARP CONDITIONS OF A NEW MATRIX SPLITTING ITERATION METHOD FOR GENERALIZED ABSOLUTE VALUE EQUATION

For the generalized absolute value equation (denoted by GAVE), we develop a new matrix splitting iteration method, which is derived by reformulating equivalently GAVE as a three-by-three block non-linear equation. Convergence of the new proposal is obtained under certain assumptions imposed on the involved iteration parameters and splitting matrix. Moreover, sharp conditions of the iteration parameters are presented via the new analysis strategy and numerical experiments also confirm the achieved theoretical results. Compared with some well-known methods, the test results show the feasibility, robustness and effectiveness of the new matrix splitting iteration method with application to the linear complementarity problem.