New convergence of modulus-based synchronous block multisplitting multi-parameter methods for linear complementarity problems

Abstract

In 2013, Bai and Zhang (Numer Linear Algebra Appl 20:425–439, 2013) constructed modulus-based synchronous multisplitting methods by an equivalent reformulation of the linear complementarity problems into a system of fixed-point equations and studied their convergence. In 2014, Zhang and Li (Comput Math Appl 67:1954–1959, 2014) analyzed and obtained the weaker convergence results for linear complementarity problems. In this paper, based on their ideas, we further study modulus-based synchronous block multisplitting multi-parameter methods for linear complementarity problems. Furthermore, the convergence results of our new method in this paper are wider than those in literature when the system matrix is a block \(H_{+}\)-matrix. Therefore, new results provide a guarantee for the optimal relaxation parameters.