A distance bound for pseudospectra of matrix polynomials
نویسنده
چکیده
In this note, we obtain a lower bound for the distance between the pseudospectrum of a matrix polynomial and a given point that lies out of it, generalizing a known result on pseudospectra of matrices.
منابع مشابه
More on pseudospectra for polynomial eigenvalue problems and applications in control theory
Definitions and characterizations of pseudospectra are given for rectangular matrix polynomials expressed in homogeneous form: P(α, β) = αAd + αd−1βAd−1 + · · · + βA0. It is shown that problems with infinite (pseudo)eigenvalues are elegantly treated in this framework. For such problems stereographic projection onto the Riemann sphere is shown to provide a convenient way to visualize pseudospect...
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The pseudospectra of a matrix polynomial P (λ) are sets of complex numbers that are eigenvalues of matrix polynomials which are near to P (λ), i.e., their coefficients are within some fixed magnitude of the coefficients of P (λ). Pseudospectra provide important insights into the sensitivity of eigenvalues under perturbations, and have several applications. First, qualitative properties concerni...
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Pseudospectra of matrix polynomials have been systematically investigated in the last years, since they provide important insights into the sensitivity of polynomial eigenvalue problems. An accurate approximation of the pseudospectrum of a matrix polynomial P (λ) by means of the standard grid method is computationally high demanding. In this paper, we propose an improvement of the grid method, ...
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ورودعنوان ژورنال:
- Appl. Math. Lett.
دوره 20 شماره
صفحات -
تاریخ انتشار 2007