منابع مشابه
Approximated structured pseudospectra
Pseudospectra and structured pseudospectra are important tools for the analysis of matrices. Their computation, however, can be very demanding for all but small matrices. A new approach to compute approximations of pseudospectra and structured pseudospectra, based on determining the spectra of many suitably chosen rank-one or projected rank-one perturbations of the given matrix is proposed. The...
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.
متن کاملStructured Pseudospectra in Structural Engineering
This paper presents a new method for computing the pseudospectra of a matrix that respects a prescribed sparsity structure. The pseudospectrum is defined as the set of points in the complex plane to which an eigenvalue of the matrix can be shifted by a perturbation of a certain size. A canonical form for sparsity preserving perturbations is given and a computable formula for the corresponding s...
متن کاملA Note on Structured Pseudospectra∗
In this note, we study the notion of structured pseudospectra. We prove that for Toeplitz, circulant and symmetric structures, the structured pseudospectrum equals the unstructured pseudospectrum. We show that this is false for Hermitian and skew-Hermitian structures. We generalize the result to pseudospectra of matrix polynomials. Indeed, we prove that the structured pseudospectrum equals the ...
متن کاملStructured Pseudospectra and Random Eigenvalues Problems in Vibrating Systems
This paper introduces the concept of pseudospectra as a generalized tool for uncertainty quantification and propagation in structural dynamics. Different types of pseudospectra of matrices and matrix polynomials are explained. Particular emphasis is given to structured pseudospectra for matrix polynomials, which offer a deterministic way of dealing with uncertainties for structural dynamic syst...
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ژورنال
عنوان ژورنال: Numerical Linear Algebra with Applications
سال: 2016
ISSN: 1070-5325
DOI: 10.1002/nla.2082