ON 2-SIDED BOUNDS RELATED TO WEAKLY DIAGONALLY DOMINANT M-MATRICES WITH APPLICATION TO DIGITAL CIRCUIT DYNAMICS

Let A be a real weakly diagonally dominant M-matrix. We establish uppe r and lower bounds for the minimal eigenvalue of A, for its correspond ing eigenvector, and for the entries of the inverse of A. Our results are applied to find meaningful two-sided bounds for both the l(1)-norm and the weighted Perron-norm of the solution x(t) to the linear diffe rential system x = -Ax, x(0) = x(0) > 0. These systems occur in a numb er of applications, including compartmental analysis and RC electrical circuits. A detailed analysis of a model for the transient behaviour of digital circuits is given to illustrate the theory.