Interval Method Of Generalized Linear Complementarity Problem

This paper research Linear complementarity problem. The main contents in this paper are as follows:With the summarizing of the research on domestic and international developments, the basic iterative methods for linear system are introduced firstly, e.g. Jacobi, Gauss-Seidel, SOR, and AOR. Then the translation of LCP to its equal form which makes the methods for linear system can be used is introduced. In the following, iterative methods for LCP, e.g. AOR, MAOR, GAOR, and two-stage iterative methods are presented. The error bounds for LCP when the system matrix is a P matrix are presented at last.According to the results of research at home and abroad, this paper investigates a special kind of Generalized-order LCP. The results of Alefeld G., Wang Z. Y. and Shen Z.H. are improved. This paper establishes an enclosure of the solution of GLCP, for which the main computational cost is to solve a system of linear system. While the two system matrices are L-matrices and strictly diagonally dominant matrices, a effective algorithm is obtained applying the enclosing iterative methods, which is able to take advantage of the high-speed computer computing and parallel computing. Then a nested sequence is obtained. The interval radius of the iterative sequences is narrowing, tending to the unique solution while the problem only has one. The midpoint of the interval is supposed to be the solution while error conditions are meted, or the conclusion of there is no solution is obtained.