Modified two-step modulus-based matrix splitting iteration methods for implicit complementarity problems

To further accelerate the convergence rate of the recent proposed modified modulus-based matrix splitting (MMMS) iteration method for solving the implicit complementarity problems, by using the two-step iteration methodology, a class of modified two-step modulus-based matrix splitting (MTMMS) iteration methods are studied in this paper. The convergence analyses of the MTMMS iteration method are carefully studied when the system matrix is a positive definite matrix or an \(H_+\) $H_{+}$ -matrix. Finally, two numerical experiments are presented. Numerical results show that the proposed MTMMS iteration method performs much better than the existing MMMS iteration method.