Modulus-based synchronous multisplitting iteration methods without auxiliary variable for solving vertical linear complementarity problems

Abstract

In this work, by applying the synchronous multisplitting technique to the non-auxiliary variable modulus equation of the vertical linear complementarity problems, a new parallel method is constructed, which can generalize the existing modulus-based matrix splitting iteration method. The convergence conditions of the proposed method are discussed in the cases of more than two system matrices, and the existing results are improved. Numerical examples under OpenACC framework show that the proposed method can solve the large sparse vertical linear complementarity problems efficiently with high parallel efficiency.