Two Kinds Of Preconditioned Methods For Solving Linear Complementarity Problem

The complementarity problem is to find a pair of non-negative functions or variables in a certain space to satisfy a complementarity relationship.This relation?ship reflects a basic relationship that exists widely.It is widely used in scientific computing and engineering applications.Complementary problem was divided into linear complementary,nonlinear complementaxity,mixed linear complementary,hor-izontal linear complementarity,generalized linear complementary etc.Simple,the form of linear complementary problem comes from engineering physics,mechan-ics,operational research and economic and other fields,in the economic balance,a non-cooperative contest,has been widely used in traffic distribution and other problems.And it is also a linear programming,double matrix game,the unification of the quadratic programming problem.Therefore,research on linear complemen-tary problem has both theoretical significance and has application value.In solving linear complementary problem,the iterative method mainly includes:Projection method,interior point method,Newton class method and the modulus-based ma-trix splitting iterative methods.This paper mainly applies GAOR method and SSOR method in projection method.In order to accelerate the convergence rate of GAOR and SSOR in solving linear complementarity problem,this paper gives the preconditioner and the convergence theory of iterative method when the coefficient matrix is M-matrix.