Natalie Wellen, University of Washington
Authors: Anne Greenbaum and Natalie Wellen
2022 AWM Research Symposium
Women in Numerical Analysis and Scientific Computing

The value of K from a K-spectral set is used to bound any analytic function of a matrix. We use results in [M. Crouzeix and A. Greenbaum, Spectral sets: numerical range and beyond, SIAM Jour. Matrix Anal. Appl., 40 (2019), pp. 1087-1101] to derive a variety of K-spectral sets and show how they can be used in some applications. We compare the K values derived here to those that can be derived from a straightforward application of the Cauchy integral formula, by replacing the norm of the integral by the integral of the resolvent norm. We show that in most cases, the two values are of the same order of magnitude.

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