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.

Abstract The merger phase of binary black hole coalescences is a transient between an initial oscillating regime (inspiral) and late exponentially damped (ringdown). In spite the non-linear character Einstein equations, dynamics presents surprisingly simple behaviour consistent with effective linearity. On other hand, energy loss through event horizon by scattering to infinity renders system no...

One of the most expensive problems in numerical linear algebra is the computation of the -pseudospectrum of matrices, that is, the locus of eigenvalues of all matrices of the form A + E, where the norm of E is bounded by . Several research efforts have been attempting to make the problem tractable by means of better algorithms and utilization of all possible computational resources. One commo...

The parallel computation of the pseudospectrum is presented. The Parallel Path following Algorithm using Triangles (PPAT) is based on the Path following Algorithm using Triangles (PAT). This algorithm offers total reliability and can handle singular points along the level curve without difficulty. Furthermore, PPAT offers a guarantee of termination even in the presence of round-off errors and m...

The real ε-pseudospectrum of a real matrix A consists of the eigenvalues of all real matrices that are ε-close in spectral norm to A. The real pseudospectral abscissa, which is the largest real part of these eigenvalues for a prescribed value ε, measures the structured robust stability of A w.r.t. real perturbations. In this report, we introduce a criss-cross type algorithm to compute the real ...

The main goal of this paper is to introduce the condition pseudospectrum multivalued linear operators and prove several relations usual spectrum. We start by giving definition then we focus on characterization, stability some their properties.

Denote by B(H) the Banach algebra of all bounded linear operators on a complex Hilbert space H. Let A ∈ B(H), and denote by σ(A) the spectrum of A. For ε > 0, define the ε-pseudospectrum σε(A) of A as σε(A) = {z ∈ σ(A+ E) : E ∈ B(H), ∥E∥ < ε}. In this paper, the pseudospectra of several special classes of operators are characterized. As an application, complete descriptions are given of the map...