Multisplitting Iterative Methods with General Weighting Matrices for Solving Symmetric Positive Linear Complementarity Problem
Abstract
In this paper, by making use of optimal models, we study the weighting matrices of the multisplitting parallel methods for solving the symmetric positive definite linear complementarity problem, which is a powerful alternative for solving the large sparse linear complementarity problems. In our multisplitting there is only one that is required to be P-regular splitting and all the others can be constructed arbitrarily, which not only decreases the difficulty of constructing the multisplitting of the coefficient matrix, but also relaxes the constraints to the weighting matrices (unlike the standard methods, they are not necessarily nonnegative diagonal scalar matrices or given in advance). Finally, we prove the convergence of this new method.
Keywords
Linear complementarity problem, Symmetric positive definite matrix, Weighting matrices, Multisplitting, Convergence
DOI
10.12783/dtcse/cmsam2017/16389
10.12783/dtcse/cmsam2017/16389
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