Step Two Anti-secession Law Solution System Of Linear Equations And Linear Complementary Problem

With the development of science and technology, many problems such as oil exploration, environmental science and aerospace are attributed to solving one or some large-scale linear equations. With the expansion of the scale of problems, the corresponding linear system of unknown numbers are also on the increase. So efficiently solving for these large linear equations becomes the key of resolving the problem. People have found several methods including Jacobi iterative method, Gauss-Seidel iterative method, SOR iterative method and JOR iterative method and so on, and search for highly efficient and rapid solution method has an important theory and practical significance. This article mainly studies the convergence of two-step splitting method for solving the linear equations.In addition, linear complementarity problems have been developed very quickly nowadays, they were widely used in engineering, economics and operations research. And this paper studies two-step splitting method for solving the linear complementary problem.This article mainly studies the convergence of GAOR method and SSOR method for the linear equations when M is an H-matrix or an M-matrix. Two-step splitting method for solving linear linear complementarity problems when M is an H+-matrix, The arrangement of this paper is as follows:In Chapter1, we briefly introduce the iterative methods for linear equations, the application of linear complementarity problems and the development of linear complementarity problems in recent decades.In Chapter2, we explain the definition of the linear equations and linear complementarity problem, and give some basic definitions, lemmas used in this paper.Chapter3is the main part of this paper. Firstly, the two-step splitting method for solving linear equations algorithm is given, and then analyze the two-step the GAOR split method for solving linear equations convergence;Secondly we study the two-step SSOR split method for the convergence of linear equations solution;Finally we outline the algorithm for the numerical example, and verify the correctness of the theorems.Chapter4is also the main part of this paper. In this section, we give a two-step iterative scheme of split method for solving linear complementarity problems, and then give the convergence theorem of the linear complementarity problem.Chapter5is a summary and outlook, which is a summary of this article and gives the prospect of GAOR method and SSOR method for solving linear equations and the two-stage splitting method for solving the linear complementarity problem.