Research Of Modified Accelerated Splitting Iteration Method For Linear Complementarity Problem

With the development of society and the progress of science and technology,a lot of numerical computation problems are produced.Linear complementarity problem occurs in a lot of numerical computation and engineering applications.With optimization of algorithms and theory for linear complementarity problem,its scope of application has been extended to finance,transportation,economy.With a lot of linear complementarity problem literature at home and abroad,mainly based on evolution method of modulus-based matrix splitting iteration method and general convergence conditions,a modified iteration method was proposed.Specific works of this essay is as follows:Firstly,introduce the linear complementarity problem,some necessary definitions,some useful lemmas,modulus-based matrix splitting iteration method and several of its evolution method.Later,based on general accelerated modulus-based matrix splitting iteration method,the convergence condition was generalized,a modified accelerated splitting iteration method was proposed.The new method can be proved to be equivalent to the linear complementarity problem theoretically and compared to other methods,a new convergence theorem with H+-matrix was put forward.Finally,with numerical examples,the new method was proved to need less iteration step numbers and shorter running time.The new method is feasible and effective.