Numerical approximation of the boundary of numerical range of matrix polynomials

Abstract

The numerical range of an n × n matrix polynomial P(λ) = A_mλ^m + A_m–1λ^m–1 + … + A₁λ + A₀ is defined by W(P) = {λ ∈ ℂ : x*P(λ)x = 0, x ∈ ℂⁿ, x*x = 1}, and plays an important role in the study of matrix polynomials. In this paper, we describe a methodology for the illustration of its boundary, ∂W(P), using recent theoretical results on numerical ranges and algebraic curves. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)