Eigenvalues, pseudospectrum and structured perturbations
نویسندگان
چکیده
منابع مشابه
Eigenvalues, Pseudospectrum and Structured Perturbations
We investigate the behavior of eigenvalues under structured perturbations. We show that for many common structures such as (complex) symmetric, Toeplitz, symmetric Toeplitz, circulant and others the structured condition number is equal to the unstructured condition number for normwise perturbations, and prove similar results for real perturbations. An exception are complex skewsymmetric matrice...
متن کاملPerturbation of purely imaginary eigenvalues of Hamiltonian matrices under structured perturbations
The perturbation theory for purely imaginary eigenvalues of Hamiltonian matrices under Hamiltonian and non-Hamiltonian perturbations is discussed. It is shown that there is a substantial difference in the behavior under these perturbations. The perturbation of real eigenvalues of real skew-Hamiltonian matrices under structured perturbations is discussed as well and these results are used to ana...
متن کاملEla Perturbation of Purely Imaginary Eigenvalues of Hamiltonian Matrices under Structured Perturbations∗
The perturbation theory for purely imaginary eigenvalues of Hamiltonian matrices under Hamiltonian and non-Hamiltonian perturbations is discussed. It is shown that there is a substantial difference in the behavior under these perturbations. The perturbation of real eigenvalues of real skew-Hamiltonian matrices under structured perturbations is discussed as well and these results are used to ana...
متن کاملToeplitz structured perturbations
We will investigate the condition number, eigenvalue perturbations and pseudospectrum of Toeplitz matrices under structured perturbations. Sometimes we will see few changes, sometimes, although provably rare, dramatic differences in the structured and unstructured view. Connections to minimization problems concerning polynomials are shown. One result is that the structured distance to the neare...
متن کاملStructured Pseudospectra for Small Perturbations
In this paper we study the shape and growth of structured pseudospectra for small matrix perturbations of the form A A∆ = A + B∆C, ∆ ∈ ∆, ‖∆‖ ≤ δ. It is shown that the properly scaled pseudospectra components converge to non-trivial limit sets as δ tends to 0. We discuss the relationship of these limit sets with μ-values and structured eigenvalue condition numbers for multiple eigenvalues.
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2006
ISSN: 0024-3795
DOI: 10.1016/j.laa.2005.06.009