The relaxed MGHSS-like method for absolute value equations

Based on the matrix splitting techniques and the ideas of the GPHSS-like method, we proposed the relaxed modified generalized HSS-like method (RMGHSS-like), which is more efficient and more robust than the RPHSS-like, the MBAS, the NI and the NHSS-like methods for the absolute value equation. Furthermore, the RMGHSS-like method is the general form of the relaxed PHSS-like method. The convergence of the RMGHSS-like iterative method is proved by theoretical analysis, and the relationships between the parameters are rigorously discussed when the coefficient matrix E is a Hermitian positive definite matrix under the minimum spectral radius. Numerical experiments had been given to recognize the effectiveness of the RMGHSS-like method.