Asynchronous multisplitting relaxation methods for linear complementarity problems

To solve the linear complementarity problems efficiently on the high-speed multiprocessor systems, we set up a class of asynchronous parallel matrix m ultisplitting accelerated overrelaxation (AOR) method by technical combinat ion of the matrix multisplitting and the accelerated overrelaxation techniq ues. The convergence theory of this new method is thoroughly established un der the condition that the system matrix of the linear complementarity prob lem is an H-matrix with positive diagonal elements. At last, we also make m ulti-parameter extension for this new asynchronous multisplitting AOR metho d, and investigate the convergence property of the resulted asynchronous mu ltisplitting unsymmetric AOR method. Thereby, an extensive sequence of asyn chronous 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 va rious choices, but also presents systematic convergence theories about the asynchronous parallel relaxation methods for solving the linear complementa rity problems.