Error Bounds Of The EVLCPs Involving Some Structured Matrices

The extended vertical linear complementarity problem(EVLCP)is a generalization of the linear complementarity problem,which has been widely used in operations research,economics and other fields.We in this thesis study the error estimation problem of the solution of the EVLCP,and obtain error bounds of the solution for the B-type matrix and the interval M-matrix cases,respectivly.Concretely,firstly,by using the properties of a B-matrix,we prove that the block matrix composed of the B-matrix has the row Wproperty,and obtain an error bound of the solution of its EVLCP.Secondly,by using the properties of a B?R-matrix,we prove that the block matrix composed of the B?R-matrix has the row W-property,and obtain an error bound for the solution of its EVLCP.Thirdly,by using the regularity and non-negative inverse property of the interval M-matrix,we prove that the block matrix composed of the interval M-matrix has the row W-property,and obtain an error bound for the solution of its EVLCP and linear complementarity problem,respectivly.Finally,by establishing the equivalent form for the solusion of the EVLCP by the diagonal matrix,a parametered error bound for the EVLCP is obtained,and some numerical examples are given to illustrate the effectiveness of the error bound.