相关论文: Spectra, Pseudospectra, and Localization for Rando…

Eigenvalues and eigenvectors of non-Hermitian tridiagonal periodic random matrices are studied by means of the Hatano-Nelson deformation. The deformed spectrum is annular-shaped, with inner radius measured by the complex Thouless formula.…

Spectral properties of Toeplitz operators and their finite truncations have long been central in operator theory. In the finite dimensional, non-normal setting, the spectrum is notoriously unstable under perturbations. Random perturbations…

M.Levitin and E.Shargorodsky purposed in a recent article, [math.SP/0212087], the use of the so called ``second order relative spectrum'', to find eigenvalues of self-adjoint operators in gaps of the essential spectrum. Let $M$ be a…

In this paper we develop and apply methods for the spectral analysis of non-self-adjoint tridiagonal infinite and finite random matrices, and for the spectral analysis of analogous deterministic matrices which are pseudo-ergodic in the…

The pseudospectra (or spectral instability) of non-selfadjoint operators is a topic of current interest in applied mathematics. In fact, for non-selfadjoint operators the resolvent could be very large outside the spectrum, making the…

This paper studies the delocalized regime of an ultrametric random operator whose independent entries have variances decaying in a suitable hierarchical metric on $\mathbb{N}$. When the decay-rate of the off-diagonal variances is…

We consider $n\times n$ non-Hermitian random matrices with independent entries and a variance profile, as well as an additive deterministic diagonal deformation. We show that their empirical eigenvalue distribution converges to a limiting…

In this paper we derive novel families of inclusion sets for the spectrum and pseudospectrum of large classes of bounded linear operators, and establish convergence of particular sequences of these inclusion sets to the spectrum or…

Random Schroedinger operators with imaginary vector potentials are studied in dimension one. These operators are non-Hermitian and their spectra lie in the complex plane. We consider the eigenvalue problem on finite intervals of length n…

Reliable and efficient computation of the pseudospectral abscissa in the large-scale setting is still not settled. Unlike the small-scale setting where there are globally convergent criss-cross algorithms, all algorithms in the large-scale…

We describe some numerical experiments which determine the degree of spectral instability of medium size randomly generated matrices which are far from self-adjoint. The conclusion is that the eigenvalues are likely to be intrinsically…

In this article we are interested for the numerical computation of spectra of non-self adjoint quadratic operators, in two and three spatial dimensions. Indeed, in the multidimensional case very few results are known on the location of the…

The approximation of the eigenvalues and eigenfunctions of an elliptic operator is a key computational task in many areas of applied mathematics and computational physics. An important case, especially in quantum physics, is the computation…

In the first part of this manuscript a relationship between the spectrum of self-adjoint operator matrices and the spectra of their diagonal entries is found. This leads to enclosures for spectral points and in particular, enclosures for…

The purpose of this note is to review some recent results concerning the pseudospectra and the eigenvalues asymptotics of non-selfadjoint semiclassical pseudo-differential operators subject to small random perturbations.

We introduce two kinds of matrix-valued dynamical processes generated by nonnormal Toeplitz matrices with the additive rank 1 perturbations $\delta J$, where $\delta \in {\mathbb{C}}$ and $J$ is the all-ones matrix. For each process, first…

A new method to enclose the pseudospectrum via the numerical range of the inverse of a matrix or linear operator is presented. The method is applied to finite-dimensional discretizations of an operator on an infinite-dimensional Hilbert…

We study the distribution of eigenvalues for selfadjoint $h$--pseudodifferential operators in dimension two, arising as perturbations of selfadjoint operators with a periodic classical flow. When the strength $\varepsilon$ of the…

We prove local convergence results for the spectra and pseudospectra of sequences of linear operators acting in different Hilbert spaces and converging in generalised strong resolvent sense to an operator with possibly non-empty essential…

The operator that first truncates to a neighborhood of the origin in the spectral domain then truncates to a neighborhood of the origin in the spatial domain is investigated in the case of Boolean cubes. This operator is self adjoint on a…