Second Order Perturbation Bounds

Abstract

With a view to studying perturbation bounds, the class of functions $f$ for which $\Vert df(A)\Vert =\Vert f^{(1)}(A)\Vert$ and $\Vert d^{(2)}f(A)\Vert =\Vert f^{(2)}(A)\Vert$, where $d^{k}f(A)$ (respectively $f^{(k)}(A)$) denotes the $k$-th Frechet (ordinary) derivative, $k=1,2$, has been investigated.