Properties Of Block Nekrasov Matrix And Its Application In Linear Complement Problems

H-matrices are widely used in numerical applied algebra,economic mathematics and optimal control theory.Many practical problems can be transformed into linear complementarity problems,and some Linear Complementarity Problems derived from practical problems involve related matrices.In recent years,many scholars at home and abroad have studied the application of H-matrices subclasses to Linear Complementarity Problems.In this paper,we study a new class of H-matrix called block Nekrasov matrices,and study the properties of block Nekrasov matrices as well as their applications to Linear Complementarity Problems.Firstly,a new subclass Nekrasov matrix of H-matrices is obtained by combining the properties of Nekrasov matrix and locally bidiagonally dominant matrix.Next,the proof of block Nekrasov matrix is given.Furthermore,we analyze the relationship between block Nekrasov matrix and other H-matrices subclasses.Secondly,the block Nekrasov matrix is divided and the upper bound of the inverse infinite norm of the block Nekrasov matrix is obtained by using the upper bound of the inverse infinite norm of the Block Nekrasov matrix.Some matrices belong to block Nekrasov matrices rather than other H-matrices.Numerical examples are given to illustrate the validity of the bounds obtained and the superiority of the bounds obtained in some matrices.Finally,the upper bound of inverse infinite norm of block Nekrasov matrix is applied to the Linear Complementarity Problem,and the error bounds of the corresponding Linear Complementarity Problem are obtained and numerical examples are given.