Research On The Iterative Algorithm Of Double Scan Modular Basis For Linear Complementarity Problems

The main content of this thesis is an investigation of two-sweep modulus-based iterative methods for linear complementarity prob-lem.Firstly,numerical iterative methods are constructed by reformu-lating the linear complementarity problem into an implicit fixed point equation.In order to solve this problem efficiently,the convergence of the relaxation general two-sweep modulus-based matrix splitting iterative method is revisited,and the range of parameters is given.Then a relaxation accelerated two-sweep modulus-based matrix split-ting iterative method is presented.In addition,the convergence of the methods is discussed when the coefficient matrix for linear com-plementarity problem is an_+-matrix.Finally,the effectiveness of the iterative methods are illustrated by numerical experiments.The contributions of this thesis include:(1)For linear complementary problem,on the basis of the re-laxation general two-sweep modulus-based matrix splitting iterative method,the convergence is further discussed.Specifically,the conver-gence conditions of the method under various selections of relaxation parameters and the corresponding range of relaxation parameters are given respectively.Numerical experiments show that the proposed method can have better numerical performance with the suitable re-laxation parameters.(2)A relaxation accelerated two-sweep modulus-based matrix s-plitting iterative method is presented.The convergence analysis illus-trates that under some conditions,the proposed method converges to the exact solution of the linear complementarity problem when the coefficient matrix is an_+-matrix.Numerical experiments show that the proposed method is more efficient than the existing ones.