Multiple Splitting Methods Matrix Of Gsaor Of The H-convergence

When undergoing numerical simulation to many practical problems in natural science and social science, People will eventually attribute these problems to one or some large sparse matrix of linear equations, such as structural designation ,calculation in numerical weather forecasting and petroleum exploration, etc. they are always used to use differential or partial differential equations as the mathematical model, however, these computing field are hign-dimension and wide–range, these pattens may probably irregular, which bring many difficulties to the calculation.With The parallel multisplitting iterative method for solving the large linear system of equations was introduced by O'Leary and White in 1985[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 the symmetric positive matrix (see [2-11]), and only a few attention was studied on the convergence, semi-convergence of the parallel multisplitting iterative method for solving the singular linear system (see [12-16]).In this paper, we further studied a new parallel multisplitting iterative method for solving the large linear system (GSAOR method) , and the attention was mainly paid to the method's convergence under the H-matrix,M-matrix condition. The arrangement of this paper is as follows. In Chapter 1, the development of the multisplitting iterative method for solving the linear system in the past few years is simply introduced.In Chapter 2, we give the definition of the multisplitting iterative method,GSAOR method, and some basic definitions, lemmas and so on are reviewed, and we present two methods, what are the multisplitting iteration algorithm and the relaxed multisplitting iteration algorithm.Chapter 3 is one of the main conclusion in this paper. We investigate the new multisplitting iterative method for the nonsingular linear equations system, in which the efficient matrix are the H-matrix,M-matrix. We also verify the validness of the multisplitting iterative method through the numerical examples.In Chapter 4 is the other main conclusion in this paper , we show when the special parameters are given, the new iterative method is simplified to the SSOR method. At the same time, we make the two-stage multisplitting for the coefficient matrix A, and take A = M ? N as the outer splitting plus M = D ? C L ? CU as the inner splitting, which using the SSOR method in the inner one, and discuss the convergence theorem for solving the linear system whose coefficient matrix are H-matrix,M-matrix. We also give numerical examples to validate the multisplitting iterative method.Chapter 5 is a summary and outlook. It summarizes the paper and makes the outlook on the multisplitting iterative method for the future.