The Estimation Of Upper Bounds For ‖A^-1‖_∞ Of Strictly α-Diagonally Dominant M-matrices

Generalized strictly diagonally dominant matrix play an important role in numerical algebra,control theory,electric system,economic mathematics and elastic dynamics and so on. But it isn't easy to determine whether the matrix is or not generalized strictly diagonally dominant matrix in reality, especially for the large matrices. Under scholar abroad and home hard work there are many important fruits.In this paper, we obtain a new better upper bound for the infinity norm of the inverse of a strictly diagonally dominant M-matrix, and give three bounds for strictly a-diagonally dominant M—matrix accordingly, and then give a numerical example to illustrate the result.In chapter three, firstly, we improve the conclusion of Wang, and give the proof in theory. Moreover, we get the bound of q(A) by q(A)=(?), then give a numerical example to illustrate the result.In chapter four, we give a bound for the inverse of strictly a-diagonally dom-inant M—matrix by using the upper bound for the inverse of a strictly diagonally dominant M—matrix obtained in chapter three, then we give a numerical example to illustrate the result.In chapter five, we give a bound for the inverse of strictly product a-diagonally dominant M—matrix by using the upper bound for the inverse of a strictly diag-onally dominant M—matrix obtained in chapter three, then we give a numerical example to illustrate the result.In chapter six, we give a bound for the inverse of strictly double product a-diagonally dominant M—matrix by using the conclusion of Pan for the inverse of a strictly double diagonally dominant matrix, then we give a numerical example to illustrate the result.