Infinite Norm Estimation Of Inverse Matrices Of Strictly Diagonally Dominant M-matrices And Its Application

Special matrix is widely used in matrix theory,optimization theory,economics,computer science and other fields.Its unique clement characteristics are not only of great-significance to its own development,but also promote the development of optimization theory and methods and other disciplines.Especially,the application of strictly diagonally dominant matrix in linear complementarity problems has attracted the attention of many researchers and it became a hot research topic.In this paper,based on the special structure and properties of strictly diagonally dominant M-matrix.the problem of upper bound estimation of the infinite norm of its inverse matrix is studied,and the upper bound estimation of the infinite norm of M-matrix which is strictly diagonally dominant is obtained.The upper bound estimation is applied to the error bound estimation of the solution of B-matrix and BS-matrix linear complementary problems.The research contents of this paper are as follows.The upper bound of the inverse matrix elements of strictly diagonally dominant M-matrix is given based on the unique element characteristics of the strictly diagonally dominant M-matrix,and a new upper bound of the infinite norm of the strictly diagonally dominant M-matrix is obtained by successive reduced order method and recursive method.The new estimator improves some recent results,and the validity of the new estimator is verified by numerical examples.A new estimator of error bound for the solution of B-matrix linear complementarity problem is obtained from a new upper bound estimator of the infinite norm of the inverse matrix of strictly diagonally dominant M-matrix.the close relationship between the B-matrix and strictly diagonally dominant M-matrix and the scaling technique of the inequality.It is proved theoretically that the new error bound estimator is better than some existing results and the feasibility and validity of the new error bound estimator are verified by numerical examples.A new error bound estimator of the solution of the linear complementarity problem of BS-matrix is given by using the new upper bound estimator of the infinite norm of the inverse matrix of M-matrix which is a strictly diagonally dominant and two important inequalities.The new estimator is proved to be better than some existing results,and the feasibility and validity of the new estimator are verified by numerical examples.