Abstract:

Based on  the range for the elements of inverse matrix, a new upper bound of the infinity norm of inverse matrix of a strictly diagonally dominant M-matrix was presented so as to obtain a lower bound of the minimum eigenvalue of the M-matrix. Meanwhile, a new upper bound of the infinity norm of inverse matrix of a strictly α-diagonally dominant M\|matrix was given. Theory analysis and numerical examples show that these bounds improve existed results.

Key words: diagonal dominance, M-matrix, upper bound, minimum eigenvalue