Some Results on Parallel Alternating Iterative Method for the Linear Complementarity Problem

Abstract

By combining alternating iterative algorithm and parallel multi-splitting, the authors set up parallel alternating iterative algorithm for solving the linear complementarity problem. It is shown that when the multi-splittings of matrix are weak nonnegative of the first type or the second type, the parallel alternating iterative algorithm is convergent. Moreover, the algorithm is also convergent when the multi-splittings are P-regular. Finally, one numerical example is given.