Abstract:

For the estimates  of ‖A^-1‖_∞ of a strictly diagonally dominant Mmatrix A, several monotone nonincreasing sequences for the upper bounds of the elements of A^-1 were given by constructing iterative format with the entries of matrix A. Thus, a sequence for the upper bounds of ‖〖A^-1‖_∞ was obtained with the aid of the upper bounds of the elements of A^-1. It is proved that the sequence is monotone nonincreasing with a lower bound ‖A^-1‖_∞ and, consequently, the sequence is convergent. The given numerical example shows that these bounds improve several existing results.

Key words: diagonally dominant, Mmatrix, inverse, upper bound, sequence