A Relaxation Two-Sweep Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems

Abstract

A general RTMS iteration method for linear complementarity problems is proposed.Choosing various pairs of relaxation parameters, we obtain new two-sweep modulus-based matrix splitting iteration methods and already known iteration procedures such as the MS [1] and TMS [27] iteration methods.If the system matrix is positive definite or an H + -matrix and the relaxation parameters ω 1 and ω 2 satisfy the inequality 0 ≤ ω 1 , ω 2 ≤ 1, sufficient conditions for the uniform convergence of MS, TMS and NTMS iteration methods are established.Numerical results show that with quasi-optimal parameters, RTMS iteration method outperforms MS and TMS iteration methods in terms of computing efficiency.