Ulm Type Algorithm For Solving Linear Complementarity Problems

The linear complementarity problem is a major theme in the study of the numerical algebra and has a wide range of applications in many fields such as Mechanics,Economics,Engineering and Transportation.In this thesis,the numerical solution of the linear complementarity problem(LCP)is investigated.For the LCP,it is first converted into a system of nonlinear equations,and then the Ulm algorithm for the solution of the operator equations is combined with the algorithm for the solution of the LCP given in[Xu W,Liu H.A modified general modulus-based matrix splitting method for linear complementarity problems of -matrices.Linear Algebra Appl,2014,458: 626-637],an Ulm-type algorithm for solving LCP is constructed,and the convergence of the given Ulm-type algorithm is discussed.This algorithm avoids the shortcoming of solving a system of linear equations in each iteration of the above algorithm,the complexity of the algorithm is reduced.Thus,the stability of the algorithm is improved.Numerical tests indicate that the algorithm given in this thesis outperforms some existing algorithms when the matrix order is large.