About H - Matrix Tor The Convergence Of Multiple Split Method

The parallel multisplitting iterative method for solving the large linear system of equations was introduced by O’Leary and White in1985[1]. From then on, this iterative method has been further studied by plenty of scholars. In the past few years, many researchers have developed the multisplitting iterations for solving the larger sparse linear systems. But the attention was mainly paid to the H-matrix、M-matrix and symmetric positive matrix (see [2-14]), only a few attention was studied on the convergence、semiconvergence of the parallel multisplitting iterative method for solving the singular linear system (see [15-21]).In this paper, we mainly studied TOR multisplitting iterative method and its relaxed iterative method for solving the large linear system, and the attention was mainly paid to the method’s convergence under the H-matrix、M-matrix condition, then we have given the application of TOR multisplitting iterative method in two-stage method.The arrangement of this paper is as follows:In Chapter1, the development of the multisplitting iterative method for solving the large linear system in the past few years is simply introduced.In Chapter2, the definition of the multisplitting iterative method, and some basic definitions, lemmas and so on are reviewed, and we present multisplitting iteration algorithm and relaxed multisplitting iteration algorithm.Chapter3is the main conclusion of this paper. We investigate the convergence of the new multisplitting iterative method for the nonsingular linear equations system under the algorithm we proposed before, in which the coefficient matrix is H-matrix or M-matrix. We also verify the validness of the multisplitting iterative method through the numerical examples.In Chapter4, we show the two-stage multisplitting method and GAOR method.At the same time, we make the two-stage multisplitting for the coefficient matrix A, and take TOR and GAOR method as the inner splitting, then discuss the convergence theorem for solving the linear system whose coefficient matrix is H-matrix or M-matrix. We also give numerical examples to validate the multisplitting iterative method.Chapter5is a summary and outlook. We give a summary of this article and an outlook of the multisplitting iterative method.