Error Bounds Of Solutions For Linear Complementarity Problems Of Several Kinds Of Matrix

The linear complementarity problem is widely used in the fields of quadratic programming,market equilibrium,and double matrix games.Therefore,the research on the linear complementarity problem of matrices is particularly important.In this thesis,the error bounds of the solutions of several kinds of matrix linear complementarity problems are mainly studied.Firstly,the error estimation problem of the solution for linear complementarity problems of S-QN matrix is studied,and a new error bound is obtained,which is proved that this error bound is not greater than the error bound in [Li J.C,Li G.Error bounds for linear complementarity problems of S-QN matrices,Numerical Algorithms,March 2020,83(3),pages 935–955].The numerical examples show that the error bound improves the above error bounds under certain conditions.Secondly,the estimations of the error bounds of the solutions of S-SOB matrix linear complementarity problems and S-OB matrix linear complementarity problems are studied,and several error bounds of S-SOB matrix linear complementarity problems and S-OB matrix linear complementarity problems are obtained.Lastly,by requiring stronger diagonal dominance for S-Nekrasov matrix and B-S-Nekrasov matrix,the strong S-Nekrasov matrix and the strong B-S-Nekrasov matrix are introduced,and error bounds of their linear complementarity problem are obtained,then discuss the asymptotic optimality of these bounds.