Black hole spectroscopy is a powerful tool to probe the Kerr nature of astrophysical compact objects and their environment. The observation multiple ringdown modes in gravitational waveforms could soon lead high-precision spectroscopy, so it critical understand if quasinormal mode spectrum stable against perturbations. It was recently shown that pseudospectrum can shed light on spectral stabili...

The spectrum of the simplest 1D convection-diffusion operator is a discrete subset of the negative real axis, but the pseudospectra are regions in the complex plane bounded approximately by parabolas. Put another way, the norm of the resolvent is exponentially large as a function of the Pdclet number throughout a certain approximately parabolic region. These observations have a simple physical ...

Motorcycles generate dissimilar sound patterns under different working conditions. Generally, the experienced mechanics in authorized service stations take test rides to hear the sounds produced to diagnose the faults. The presented work attempts to locate the faults in motorcycles based on the sound. The features are extracted using pseudospectra of sound signals. Integration is performed for ...

We give a mathematically rigorous analysis which confirms the surprising results in a recent paper [2] of Benilov, O’Brien and Sazonov about the spectrum of a highly singular non-self-adjoint operator that arises in a problem in fluid mechanics. MSC-class: 34Lxx, 76Rxx, 65F15, 65Q05 keywords: spectrum, non-self-adjoint, fluid mechanics, pseudospectra, eigenvalue, basis.

Abstract. The computation of the structured pseudospectral abscissa and radius (with respect to the Frobenius norm) of a Toeplitz matrix is discussed and two algorithms based on a low rank property to construct extremal perturbations are presented. The algorithms are inspired by those considered in [GO11] for the unstructured case, but their extension to structured pseudospectra and analysis pr...

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...

we define a new type of spectrum, called δ-approximate spectrum, of an element a in a complex unital banach algebra a and show that the δ-approximate spectrum σ_δ (a) of a is compact. the relation between the δ-approximate spectrum and the usual spectrum is investigated. also an analogue of the classical gleason-kahane-zelazko theorem is established: for each ε>0, there is δ>0 such that if ϕ is...

The structured pseudospectra of a matrix A are sets of complex numbers that are eigenvalues of matrices X which are near to A and have the same entries as A at a fixed set of places. The sum of multiplicities of the eigenvalues of X inside each connected component of the structured pseudospectra of A does not depend on X. This fact is known, but not so much as it should be. For this reason, we ...

This work focuses on non-square matrix pencils A − λB where A,B ∈ Mm×n and m > n. Traditional methods for solving such nonsquare generalized eigenvalue problems (A−λB)v = 0 are expected to lead to no solutions in most cases. In this paper we propose a different treatment; We search for the minimal perturbation to the pair (A,B) such that these solutions are indeed possible. Two cases are consid...

The spectrum of the simplest 1D convection-diiusion operator is a discrete subset of the negative real axis, but the pseudospectra are regions in the complex plane bounded approximately by parabolas. Put another way, the norm of the resolvent is exponentially large as a function of the P eclet number throughout a certain approximately parabolic region. These observations have a simple physical ...