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Global relaxed modulus-based synchronous block multisplitting multi-parameters methods for linear complementarity problems
Li-Tao Zhang
Keywords:Global relaxed modulus-based method; Linear complementarity problem; Block multisplitting; Block H+?matrix; Synchronous multisplitting
Abstract:
      Recently, Bai and Zhang [Numerical Linear Algebra with Applications, 20(2013):425439] constructed modulus-based synchronous multisplitting methods by an equivalent reformulation of the linear complementarity problem into a system of ?xed-point equations and studied the convergence of them; Li et al. [Journal of Nanchang University (Natural Science), 37(2013):307-312] studied synchronous block multisplitting iteration methods; Zhang and Li [Computers and Mathematics with Application, 67(2014):1954-1959] analyzed and obtained the weaker convergence results for linear complementarity problems. In this paper, we generalize their algorithms and further study global relaxed modulus-based synchronous block multisplitting multi-parameters methods for linear complementarity problems. Furthermore, we give the weaker convergence results of our new method in this paper when the system matrix is a block H+?matrix. Therefore, new results provide a guarantee for the optimal relaxation parameters, please refer to [A. Hadjidimos, M. Lapidakis and M. Tzoumas, SIAM Journal on Matrix Analysis and Applications, 33(2012):97-110, (dx.doi.org/10.1137/100811222)], where optimal parameters are determined.