Structured Pseudospectra for Polynomial Eigenvalue Problems, with Applications
نویسندگان
چکیده
منابع مشابه
Structured Pseudospectra for Polynomial Eigenvalue Problems, with Applications
Pseudospectra associated with the standard and generalized eigenvalue problems have been widely investigated in recent years. We extend the usual definitions in two respects, by treating the polynomial eigenvalue problem and by allowing structured perturbations of a type arising in control theory. We explore connections between structured pseudospectra, structured backward errors, and structure...
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Minimal structured perturbations are constructed such that an approximate eigenpair of a nonlinear eigenvalue problem in homogeneous form is an exact eigenpair of an appropriately perturbed nonlinear matrix function. Structured and unstructured backward errors are compared. These results extend previous results for (structured) matrix polynomials to more general functions. Structured and unstru...
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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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A detailed structured backward error analysis for four kinds of Palindromic Polynomial Eigenvalue Problems (PPEP) ( d ∑ l=0 Alλ l ) x = 0, Ad−l = εA ⋆ l for l = 0, 1, . . . , ⌊d/2⌋, where ⋆ is one of the two actions: transpose and conjugate transpose, and ε ∈ {±1}. Each of them has its application background with the case ⋆ taking transpose and ε = 1 attracting a great deal of attention lately ...
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ژورنال
عنوان ژورنال: SIAM Journal on Matrix Analysis and Applications
سال: 2001
ISSN: 0895-4798,1095-7162
DOI: 10.1137/s0895479800371451