Tor Method And Gsaor The Convergence Of Solutions Of Linear Complementary Problem

Linear complementarity problems have been developed very quickly since they appeared in the60s last century, especially the recent two decades. And they comes into being a system with their theories, algorithms and applications.The theory of the linear complementarity problems is devoted to study the existence, uniqueness, stability and sensitivity analysis of the solutions, while the algorithm study is intended to solve the problems efficiently with the theoretical analysis together. And the applications of problems are widely used in engineering, economics and operational research.This article mainly studies the convergence of two TOR methods and GSAOR method for the linear complementary problems when M is an H+-matrix or an M-matrix. The arrangement of the paper is as follows:In Chapter1, we introduce the development and application of the linear complementarity problems in recent decades briefly.In Chapter2, we explain the definition of the TOR method, and give some basic definitions, lemmas used in this paper.Chapter3is the main part of the paper. Firstly, we give two algorithms of TOR method for solving the linear complementarity problems, and prove the convergence theorem when M is an H+-matrix or an M-matrix;Moreover, when M is an L-matrix, we discuss the monotone convergence of the two methods;Finally, we verify the validness of the corresponding theorems through the numerical examples.Chapter4is another main part of the paper. In this section, we from TOR method get the algorithm of GSAOR method for solving the linear complementarity problems;then get GSSOR method.Then we give the convergence theorems of the two method; Moreover, when M is an L-matrix, we discuss the monotone convergence of the two methods;Finally, we verify the validness of the corresponding theorems through the numerical examples.Chapter5is the summary and outlook, which has done a summary of this article and given the prospect of TOR methods and GSAOR method for solving the linear complementarity problems in the future.