Error Bounds For Some Kinds Of Special Matrices With Linear Complimentarity Problem

The linear complementarity problem LCP(M,q) which is widely used in t-he optimiztion problem is very important in economics, game theory and math-smatical programming. The existence and uniqueness of solution of LCP, sensi-tivity and the convergence of algorithm are related to the structures and prope-rties of the M matrix. Recently, estimation of the error bounds of solution for linear complementarity problem is a hot research topic in complementarity pro-blem research field. This paper mainly studied the error bounds estimation of solutions for the linear complementarity problem of three kinds of matrices which include the S-Nekrasov matrix, double a-chain diagonally dominant matrix and MB matrix.In chapter 1, we not only show the background and significance of the s-;lected topic, but also introduce the main work about this paper.In chapter 2, we mainly research the error bounds for S-Nekrasov matrics with linear complimentarity problem. This chapter mainly study the positive di-agonal element of non-singular matrix S-Nekrasov matrix. We deform the form-ulation of definition, then get a interval parameter.According to the properties of H matrix we get a new error bound of linear complimentarity problem. Fin-ally their mutual independence is illustrated by some numerical examples.In chapter 3, we focus on error bounds for double α-chain diagonally d-ominant matrices with linear complimentarity problem. By using the properties of matrix element, the combination of inequality techniques and then derive a new error bound. At last preliminary numerical results show that the proposed error bound is efficient for verifying accuracy of approximate solutions.In chapter 4,we introduce error bounds for MB matrices with linear com-plimentarity problem. MB matrix is decomposed into to B++C by the propert-yes of it, then constructing a monotone increasing function.According the funct-ion monotonicity we get the upper bound of the function.Finally,we get a new srror bound and numerical example is given to illustrate the effectiveness of the error bounds.In chapter 5, summarizes the work we had done, point out that the defe-cts existing in the work and the future prospects of research work.