Abstract
In 2013, Bai and Zhang [<i>Numerical Linear Algebra with Applications</i>, 20(2013):425-439] constructed modulus-based synchronous multisplitting methods by an equivalent reformulation of the linear complementarity problems into a system of fixed-point equations and studied the convergence of them. In 2014, Zhang and Li [<i>Computers and Mathematics with Application</i>, 67(2014):1954-1959] analyzed and obtained the weaker convergence results for linear complementarity problems. In 2008, Zhang et.al. [<i>International Journal of Computer Mathematics</i>, 85(2)(2008):211-224] presented global relaxed non-stationary multisplitting multi-parameter method by introducing some relaxed parameters. In this paper, we generalize Bai and Zhang's methods and study relaxed modulus-based synchronous multisplitting multi-parameters TOR (two-parameters over-relaxation, abbreviated as TOR) methods for linear complementarity problems. Furthermore, the convergence results of our new method in this paper are given when the system matrix is an $H_{+}-$matrix.
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