Modified quasi-Chebyshev acceleration to nonoverlapping parallel multisplitting method

In this study, we propose a modified quasi-Chebyshev acceleration to the nonoverlopping multisplitting iteration method for solving the linear systems Ax = b where A is a real symmetric positive definite matrix or an H-matrix. In the process of the parallel multisplitting method, the distributive tasks are parallelly computed by each processor, then a global modified acceleration is used to obtain the solution of the system Ax = b for every τ steps, such that the efficiency of the computation can be improved. The convergence theory of the new algorithm is given under some reasonable conditions. Finally, numerical experiments show that the method is efficient and effective.

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