Optimal Gersgorin-style estimation of extremal singular values

Our purpose is to identify matrices that extremize the maximum and minimum singular values among all matrices that share one of two types of Gersgorin data. All matrices sharing one type of information are treated equally, and no other information is taken into account. Knowledge of extremizers provides optimal estimates. Examples are given. As the largest singular value is also an operator norm induced by an absolute vector norm, we mention analogous facts for other operator norms.