Polynomial eigenvalue estimation: numerical radii versus norms
A. Melman · Linear and Multilinear Algebra · 2021
Bounds on the moduli of polynomial eigenvalues are typically expressed in terms of norms of the coefficient matrices of the polynomials. It is shown that using the numerical radii of these matrices instead of their norms can lead to improvements of those bounds and also, in special cases, to information on the angular distribution of the eigenvalues.