The spectral analysis of the matrix multisplitting method for the one-dimensional model problem

For the system of linear equations resulting from the discretization of the one-dimensional Poisson equation, we investigate the influences of the multiple splittings and the weighting matrices upon the convergence rate of the parallel matrix multisplitting method. The results show that the convergence rate is only dependent on the sizes of the splittings, the degrees of the overlappings, and the distributions of the tasks, but independent of the quantities of the weightings.