A parallel multisplitting method with self-adaptive weightings for solving H-matrix linear systems

In this paper, a parallel multisplitting iterative method with the self-adaptive weighting matrices is presented for the linear system of equations when the coefficient matrix is an H-matrix. The zero pattern in weighting matrices is determined in advance, while the non-zero entries of weighting matrices are determined by finding the optimal solution in a hyperplane of α points generated by the parallel multisplitting iterations. Especially, the nonnegative restriction of weighting matrices is released. The convergence theory is established for the parallel multisplitting method with self-adaptive weightings. Finally, a numerical example shows that the parallel multisplitting iterative method with the self-adaptive weighting matrices is effective.