A class of two-step modulus-based matrix splitting iteration methods for quasi-complementarity problems

Abstract

In this paper, a class of two-step modulus-based matrix splitting (TMMS) iteration methods are proposed to solve the quasi-complementarity problems. In the new TMMS iteration method, we first use the modulus technique to equivalently transform the quasi-complementarity problem into a fixed point equation, and then construct a class of two-step matrix splitting iteration methods to further accelerate the convergence rates. Theoretical results show that the proposed TMMS iteration methods are global convergent under certain conditions when the system matrix is either a positive definite matrix or an $$H_+$$-matrix. Finally, two numerical examples are presented to demonstrate that the TMMS iteration methods are superior to some existing modulus-based iteration methods studied recently for solving the quasi-complementarity problems.