Convergence analysis of the parallel multisplitting TOR method

In this paper, we propose the parallel multisplitting TOR method, for solving a large nonsingular systems of linear equations Ax = b. These new methods are a generalization and an improvement of the relaxed parallel multisplitting method (Formmer and Mager, 1989) and parallel multisplitting AOR Algorithm (Wang Deren, 1991). The convergence theorem of this new algorithm is established under the condition that the coefficient matrix A of linear systems is an H-matrix. Some results also yield new convergence theorem for TOR method.