Saor And Gaor Method 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 were widely used in engineering, economics and operations research. Roughly speaking, the study of the linear complementarity problems can be classified into two classes:theories and algorithms. The former is devoted to the existence, uniqueness, stability and sensitivity analysis of the solutions, while the latter is intended to solve the problems efficiently, together with the theoretical analysis of the algorithms.This article mainly study the convergence of two SAOR methods and two GAOR methods for linear complementary problems when M is an H+-matrix or an M-matrix. The arrangement of this paper is as follows:In Chapter1, we briefly introduce 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 complementarity problem, and give some basic definitions, lemmas used in this paper.Chapter3is the main conclusion of this paper. Firstly, we give two algorithms of SAOR method for solving linear complementarity problems, proved the convergence theorem when M is an H+-matrix or an M-matrix. Moreover, when M is an L-matrix, we discussed the monotone convergence of this two methods. Finally, we verify the validness of the corresponding theorems through numerical examples.Chapter4is also the main conclusion of this paper. In this section, we show the two GAOR iterative formats for solving linear complementarity problems when the special parameters α=γ/ω, Ω=ωI are given. Then we give the convergence theorems of the GAOR method for solving linear complementarity problems. 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 numerical examples.Chapter5is a summary and outlook, which has done a summary of this article and given the prospect of SAOR methods and GAOR methods for solving linear complementarity problems.