The Upper Bound Of Inverse Matrix Norm Of S-type Strictly Diagonally Dominant Matrix And Its Application In Linear Complementarity Problems

H-matrix is widely applied to computational mathematics,economic mathematics,and control theory.The solution of many practical problems can be transformed into solving Linear Complementarity Problems,and some Linear Complementarity Problems derived from actual problems involve related H-matrix.In recent years,many domestic and foreign scholars have studied the application of subclasses of H-matrices in Linear Complementarity Problems.In this paper,we study the upper bound of the infinite norm of the inverse matrix of the S-type strictly diagonally dominant matrix in subclasses of the H-matrix and its application in Linear Complementarity problems.Firstly,we obtain the Schur complement of the specific sub-matrix of the S-type strictly diagonally dominant matrix is also strictly diagonally dominant by using the properties of the permutation matrix and combining with the related theories of Hmatrix,M-matrix,and nonnegative matrix.Furthermore,the diagonal dominance degree of its Schur complement is obtained via appropriate inequality scaling techniques.Secondly,we should convert the S-type strictly diagonally dominant matrix into a block diagonal matrix composed of a specific sub-matrix and its Schur complement,and exert the upper bound of the infinite norm of the inverse matrix of the strictly diagonally dominant matrix,the properties of the infinite norm and the diagonally dominant degree obtained above,to obtain the upper bound of the infinite norm of the inverse matrix of the strictly diagonally dominant matrix of S-type strictly diagonally dominant matrix.Numerical examples,compared with recent related results,illustrate the superiority of our results.Finally,we apply the newly obtained inverse matrix infinite norm upper bound of S-type strictly diagonally dominant matrix applyed to the error bound of the Linear Complementarity Problems,and the corresponding new results are obtained.We select100 S-type strictly diagonally dominant matrices with positive diagonal elements for numerical comparison,and conclude that our bounds are better than existing bounds in many cases.