Error Bound Estimation For Linear Complementarity Problems Of Some Special Matrices

In the 1960s,the linear complementarity problem was proposed by G.B.Dantzig and R.W.Cottle and then it came into the field of vision of the vast number of scholars.It has been applied in the fields of mechanics,finance,control and numerical algebra.The weak chain diagonally dominant B-matrix,B~S-matrix,Dashnic-Zusmanovich matrix and other special matrices of numerical algebra problems play an extremely important role in the application.In recent years,special matrices have attracted more and more scholars and experts to study it,the literatures about error bound estimation for linear complementarity problems of special matrices become more and more.In this paper,we study the error bound estimation for linear complementarity problem of weak chain diagonally dominant B-matrix,B~S-matrix,Dashnic-Zusmanovich matrix.Some new estimates are obtained and compared it to the results which are obtained by other scholars.Firstly,a new estimation formula of error bounds for linear complementarity problem of weak chain diagonally dominant B-matrices.According to the infinite norm range of the inverse matrix of the weak chain diagonally dominant M-matrix,a new estimate of the error bound for the linear complementarity problem of the weak chain diagonally dominant B-matrix is obtained.Through the comparison of theoretical proof and numerical examples,we can know that the new estimate improve the existing results.Then,a new estimation formula of error bounds for linear complementarity problem of B~S-matrix.According to the infinite norm range of the inverse matrix of the strictly diagonally dominant M-matrix,a new upper bound of error bound for linear complementarity problem of theB~S-matrix is obtained.Numerical examples are given to show that the new upper bound is superior to the existing results in some literatures.Finally,a new estimation formula of error bounds for linear complementarity problem of Dashnic-Zusmanovich matrix is presented.By using the infinite norm range of the inverse matrix of the Dashnic-Zusmanovich matrix,the new error bound estimate for linear complementarity problem of Dashnic-Zusmanovich matrix can be obtained by theoretical proof.We can know it that the estimate is better than the existing results by numerical examples.