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• W2046982553 abstract "For a given square matrix A and positive integer k, we consider sets Ω in the complex plane satisfying∥p(A)∥⩾maxz∈Ω|p(z)|for all polynomials p of degree k or less. The largest such set, referred to as the polynomial numerical hull of degree k, was introduced by O. Nevanlinna [Convergence of Iterations for Linear Equations, Birkhäuser, Basel, 1993] and a number of properties of this set were derived for both matrices and linear operators. We give several equivalent characterizations of the polynomial numerical hull of degree k and we actually compute these sets for several matrices. For k=1, this set is just the field of values of A, and for k⩾m, where m is the degree of the minimal polynomial of A, it is the spectrum of A. For 1<k<m, these sets are intermediate between the field of values and the spectrum and sometimes resemble pseudospectra." @default.
• W2046982553 created "2016-06-24" @default.
• W2046982553 creator A5019550551 @default.
• W2046982553 date "2002-05-01" @default.
• W2046982553 modified "2023-09-27" @default.
• W2046982553 title "Generalizations of the field of values useful in the study of polynomial functions of a matrix" @default.
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• W2046982553 doi "https://doi.org/10.1016/s0024-3795(01)00555-9" @default.
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