The sharpness of stability estimates corresponding to a general resolvent condition Original Research Article

In the stability analysis of numerical processes the problem arises of establishing (moderate) upper bounds for the norm of the nth power of given s×s matrices. Recently, new upper bounds were derived under generalized versions of the resolvent condition occurring in the Kreiss matrix theorem. In the present paper, the question is answered of whether these new bounds are sharp, with respect to their behaviour as n→∞ and s→∞.