Error Bounds For The Linear Complementarity Problems Of Some Classes Of Structured Matrices

Linear complementarity problems LCP(M,q)are widely used in economics,finance,linear programming and other fields,the existence and uniqueness of the solution of LCP,sensitivits,and the convergence of the algorithms are all related to the structures and properties of the matrix M.This thesis mainly studies error bounds for the solutions for linear complementarity problems when the matrix Mare Dashnic-Zusmaovich(DZ)matrices,Dashnic-Zusmanovich-B(DZ-B)matrices and double strictly diagonally dominant(DSDD)matrices,and we get some upper bounds which depend only on the elements of M.The specific content is as follows.In Chapter 2,the error boundary estimation of linear complementary problems of DZ matrix and DZ-B matrix is studied.The new error estimation formula are obtained by using the upper bounds of the infinity norms of the inverse matrix of DZ matrices,the special structure and properties of DZ matrices and the monotonicity of functions.Some numerical examples are also given to show the validity of the results.In Chapter 3,the optimal error bounds for the linear complementarity problem of DSDD matrices are studied.For the error bound of the H-matrix linear complementarity problem proposed in[M.Garcia-Esnaola,J.M.Pena.A comparison of error bound s for linear complementarity problems of H-matrices.Linear Algebra Appl,2010,433(5):956-964],by using the properties of the DSDD matrix and the monotonicity of the function,the optimal value of the error bound with a parameter of linear complementarity problem of DSDD matrices is given.Finally,some numerical examples are given to verify the corresponding results.