Asynchronous multisplitting relaxation methods for linear complementarity problems

Abstract

To solve the linear complementarity problems efficiently on the high-speed multiprocessor systems, we set up a class of asynchronous parallel matrix multisplitting accelerated over-relaxation (AOR) method by technical combination of the matrix multisplitting and the accelerated overrelaxation techniques. The convergence theory of this new method is thoroughly established under the condition that the system matrix of the linear complementarity problem is an H-matrix with positive diagonal elements. At last, we also make multi-parameter extension for this new asynchronous multisplitting AOR method, and investigate the convergence property of the resulted asynchronous multisplitting unsymmetric AOR method. Thereby, an extensive sequence of asynchronous parallel relaxed iteration methods in the sense of multisplitting is presented for solving the large scale linear complementarity problems in the asynchronous parallel computing environments. This not only affords various choices, but also presents systematic convergence theories about the asynchronous parallel relaxation methods for solving the linear complementarity problems.