Numerical bounds on the Crouzeix ratio for a class of matrices
Résumé
We provide numerical bounds on the Crouzeix ratio
for KMS matrices $A$ which have a line segment on the boundary
of the numerical range. The Crouzeix ratio is the supremum
over all polynomials $p$ of the spectral norm of $p(A)$ divided
by the maximum absolute value of $p$ on the numerical range of $A$.
Our bounds confirm the conjecture that this ratio
is less than or equal to $2$. We also give a precise description of these numerical ranges.
Domaines
Mathématiques générales [math.GM]
Origine : Fichiers produits par l'(les) auteur(s)