Structured pseudospectra for nonlinear eigenvalue problems
نویسندگان
چکیده
منابع مشابه
Backward errors and pseudospectra for structured nonlinear eigenvalue problems
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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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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Let λ be a nonderogatory eigenvalue of A ∈ C. The sensitivity of λ with respect to matrix perturbations A A + ∆,∆ ∈ ∆, is measured by the structured condition number κ∆(A,λ). Here ∆ denotes the set of admissible perturbations. However, if ∆ is not a vector space over C then κ∆(A, λ) provides only incomplete information about the mobility of λ under small perturbations from ∆. The full informati...
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An inverse eigenvalue problem concerns the reconstruction of a structured matrix from prescribed spectral data. Such an inverse problem arises in many applications where parameters of a certain physical system are to be determined from the knowledge or expectation of its dynamical behavior. Spectral information is entailed because the dynamical behavior often is governed by the underlying natur...
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Most eigenvalue problems arising in practice are known to be structured. Structure is often introduced by discretization and linearization techniques but may also be a consequence of properties induced by the original problem. Preserving this structure can help preserve physically relevant symmetries in the eigenvalues of the matrix and may improve the accuracy and efficiency of an eigenvalue c...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2008
ISSN: 0377-0427
DOI: 10.1016/j.cam.2006.12.007