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 ...

This paper presents a novel model-based method for in-situ estimation of sound reflection coefficients in acoustic enclosures. The method uses a modeling engine for simulation of acoustic propagation and generation of the spatial pseudospectrum using a beamforming technique. The simulated pseudospectrum is matched with the measured pseudospectrum acquired by a real beamforming microphone array ...

In an earlier report 4], the pseudospectrum of the rst derivative operator discretized by spectral and nite diierence methods has been analyzed. Here, the same work is carried out for the convection-diiusion operator. The high sensitivity of the pseudospectrum of the operator under several discretization methods is illustrated by numerous examples.

The pseudospectrum descent method (PsDM) is proposed, a new parallel method for the computation of pseudospectra. The idea behind the method is to use points from an already existing pseudospectrum level curve oK to generate in parallel the points of a new level curve oKd such that d < . This process can be continued for several steps to approximate several pseudospectrum level curves lying ins...

We define and evaluate the normwise backward error and condition numbers for the multiparameter eigenvalue problem (MEP). The pseudospectrum for the MEP is defined and characterized. We show that the distance from a right definite MEP to the closest non right definite MEP is related to the smallest unbounded pseudospectrum. Some numerical results are given.

This report was written in 2001 and it is a translation of work that was originally published in Greek, in the author’s diploma thesis in July 1998. It may contain minor mistakes and should not be considered a complete study. It however touches upon several of the considerations that will be included in the complete paper. The work was done jointly with E. Gallopoulos and was presented at the F...

The aim of this paper is twofold: On the one hand, we suggest a characterization for left (right) condition pseudospectrum bounded linear operators. other give an analogue spectral mapping theorem pseudospectrum.

The pseudospectrum descent method (PsDM) is proposed, a new parallel method for the computation of pseudospectra. The idea behind the method is to use points from an already existing pseudospectrum level curve oK to generate in parallel the points of a new level curve oKd such that d < . This process can be continued for several steps to approximate several pseudospectrum level curves lying ins...

Dedicated to Professor Hans Schneider. Abstract The interplay between the algebraic and analytic properties of a matrix and the geometric properties of its pseudospectrum is investigated. It is shown that one can characterize Hermitian matrices, positive semi-definite matrices, orthogonal projections, unitary matrices, etc. in terms of the pseudospectrum. Also, characterizations are given to ma...