A preconditioned two-step modulus-based matrix splitting iteration method for linear complementarity problem

Abstract In this paper, a preconditioned two-step modulus-based matrix splitting iteration method for linear complementarity problems associated with an M-matrix is proposed. The convergence analysis of the presented method is given. In particular, we provide a comparison theorem between preconditioned two-step modulus-based Gauss–Seidel (PTMGS) iteration method and two-step modulus-based Gauss–Seidel (TMGS) iteration method, which shows that PTMGS method improves the convergence rate of original TMGS method for linear complementarity problem. Numerical tested examples are used to illustrate the theoretical analysis.

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