Abstract A new method to enclose the pseudospectrum via numerical range of inverse a matrix or linear operator is presented. The applied finite-dimensional discretizations an on infinite-dimensional Hilbert space, and convergence results for different approximation schemes are obtained, including finite element methods. We show that full contained in intersection sets which expressed terms rang...

The construction of an accurate approximation of the-pseudospectrum of a matrix by means of the standard grid method is a very demanding computational task. In this paper, we describe Cobra, a domain-based method for the computation of pseudospectra that combines predictor corrector path following with a one-dimensional grid. The algorithm o€ers large and medium grain parallelism and becomes pa...

We consider the real ε-pseudospectrum of a real square matrix, which is the set of eigenvalues of all real matrices that are ε-close to the given matrix, where closeness is measured in either the 2-norm or the Frobenius norm. We characterize extremal points and compare the situation with that for the complex ε-pseudospectrum. We present differential equations for rank-1 and rank2 matrices for t...

The -pseudospectrum of a square matrix A is the set of eigenvalues attainable when A is perturbed by matrices of spectral norm not greater than . The pseudospectral abscissa is the largest real part of such an eigenvalue, and the pseudospectral radius is the largest absolute value of such an eigenvalue. We find conditions for the pseudospectrum to be Lipschitz continuous in the setvalued sense ...

In this paper, we study the ε-lemniscate of the characteristic polynomial in relation to the pseudospectrum of the associated matrix. It is natural to investigate this question because these two sets can be seen as generalizations of eigenvalues. The question of numerical determination of the ε-lemniscate raises the problem of computing the characteristic polynomial p. We can express the coeffi...

We present several new techniques for approximating spectra and pseudospectra of linear operators (not necessarily bounded) on a separable Hilbert space. This includes new results on the finite section method (and some variants of it) as well a generalization of the QR algorithm to infinite dimensions. In order to approximate spectra of arbitrary closed operators we introduce a generalization o...

We describe the spectra and pseudospectra of continuous time and discrete time waveform relaxation operators. Since the spectrum of the finite-interval waveform relaxation operator is only a singleton, the spectrum of the infinite-interval operator is typically used to describe the behavior of waveform relaxation algorithms. Here, we show that the pseudospectrum is a more useful tool for analyz...

In this paperwe investigate the spectrum and Drazin their pseudo spectral analogues, for linear relations between Banach spaces corresponding spectra, generalized Drazinmeromorphic pseudospectrum. More specifically, Drazin-meromorphic pseudospectrum a on space is studied. We also make several observations about level set of relations. Furthermore, it shown that has no isolated points, finite nu...