Let $A$ be an $n \times n$ matrix. Define the field of values of $A$, denoted $W(A)$, as

$ W(A) := \{c \in \mathbb{C} : \exists x \in \mathbb{C}^n, \|x\|_2 = 1, x^H Ax = c \} $

The question is, suppose one knows the spectra and singular values of $A$, are there any nontrivial bounds for the distance between an eigenvalue $\lambda$ and the edge of the field of values $\partial W(A)$?