A general modulus-based matrix splitting method for quasi-complementarity problem

For large sparse quasi-complementarity problem (QCP), Wu and Guo ^[35] recently studied a modulus-based matrix splitting (MMS) iteration method, which belongs to a class of inner-outer iteration methods. In order to improve the convergence rate of the inner iteration so as to get fast convergence rate of the outer iteration, a general MMS (GMMS) iteration method is proposed in this paper. Convergence analyses on the GMMS method are studied in detail when the system matrix is either an $H_{+}$-matrix or a positive definite matrix. In the case of $H_{+}$-matrix, weaker convergence condition of the GMMS iteration method is obtained. Finally, two numerical experiments are conducted and the results indicate that the new proposed GMMS method achieves a better performance than the MMS iteration method.