Distance problems for hermitian matrix polynomials an epsilon pseudospectra based approach

Abstract

Definite and definitizable pencils and hyperbolic quasihyperbolic and definite polynomi als are Hermitian matrix polynomials with real eigenvalues of definite type that arise in many applications in science and engineering Given a member of any of these classes it is therefore of practical importance to know the distance to a nearest Hermitian polyno mial outside the class These distance problems are analysed with respect to a specific norm in the setting of Hermitian pseudospectra of thes