A bivariate extension of the Crouzeix-Palencia result with an application to Fréchet derivatives of matrix functions

Michel Crouzeix, Daniel Kressner

A result by Crouzeix and Palencia states that the spectral norm of a matrix function $f(A)$ is bounded by $K=1+\sqrt{2}$ times the maximum of $f$ on $W(A)$, the numerical range o…