Upper Bound Estimations Of The Infinity Norm For The Inverse Of Special Matrices

The infinity norm of inverse of special matrices plays very important role in theory and practical application and it has unique charm.For example,in economic mathematics,physics,biological mathematics and other disciplines applied.When the order of moment matrices is very large,it is very difficult to obtain their inverse matrices,under the circumstances,it is convenient to use the upper bound estimation of the infinity norm of the inverse matrices of the special matrices instead of the real value for calculation.So it is very necessary to find the upper bound estimator of the inverse infinity norm of matrices in practical application.In this thesis,we study the infinity norm upper bounds estimation of the inverse of some special subclass matrices of H-matrices.the infinity norm upper bound estimators for the more accurate inverse of strictly diagonally dominant M-matrices,strictly ?2-diagonally dominant matrices and Nekrasov matrices are given,and the validity of the estimators is illustrated by numerical examples.Secondly,use elements of the matrices characteristics,a combination of inequality techniques,the estimation formula of ?A-1?? of SDD matrix A is given.For the infinity norm bound of the inverse matrix of strictly ?2-diagonally dominant Mmatrix,according to the element characteristics of the matrix,the matrix A is split into the form of F,G.And with the aid of the infinity norm of inverse matrix of strictly diagonally dominant matrix estimate to ?F-1??,thus,the improved estimation of?A-1?? is obtained.