NLEVP: A collection of nonlinear eigenvalue problems
We present a collection of 52 nonlinear eigenvalue problems in the form of a MATLAB
toolbox. The collection contains problems from models of real-life applications as well as …
toolbox. The collection contains problems from models of real-life applications as well as …
Spectral pollution and how to avoid it
This paper, devoted to the study of spectral pollution, contains both abstract results and
applications to some self-adjoint operators with a gap in their essential spectrum, occurring …
applications to some self-adjoint operators with a gap in their essential spectrum, occurring …
Spectral pollution and eigenvalue bounds
L Boulton - Applied Numerical Mathematics, 2016 - Elsevier
The Galerkin method can fail dramatically when applied to eigenvalues in gaps of the
extended essential spectrum. This phenomenon, called spectral pollution, is notoriously …
extended essential spectrum. This phenomenon, called spectral pollution, is notoriously …
Spurious modes in Dirac calculations and how to avoid them
In this paper we consider the problem of the occurrence of spurious modes when computing
the eigenvalues of Dirac operators, with the motivation to describe relativistic electrons in an …
the eigenvalues of Dirac operators, with the motivation to describe relativistic electrons in an …
Generalized Weyl theorems and spectral pollution in the Galerkin method
We consider a general framework for investigating spectral pollution in the Galerkin method.
We show how this phenomenon is characterised via the existence of particular Weyl …
We show how this phenomenon is characterised via the existence of particular Weyl …
On the limit behaviour of second order relative spectra of self-adjoint operators
E Shargorodsky - Journal of Spectral Theory, 2013 - ems.press
It is well known that the standard projectionmethods allow one to recover the whole
spectrum of a bounded self-adjoint operator but they often lead to spectral pollution, ie to …
spectrum of a bounded self-adjoint operator but they often lead to spectral pollution, ie to …
On the computation of the eigenvalues of Dirac systems
MH Annaby, MM Tharwat - Calcolo, 2012 - Springer
The main purpose of this paper is to compute the eigenvalues of Dirac systems using a
regularized sampling method. The operator examined here is the massless Dirac operator …
regularized sampling method. The operator examined here is the massless Dirac operator …
On the convergence of second-order spectra and multiplicity
L Boulton, M Strauss - Proceedings of the Royal Society …, 2011 - royalsocietypublishing.org
The notion of second-order relative spectrum of a self-adjoint operator acting on a Hilbert
space has been studied recently in connection with the phenomenon of spectral pollution in …
space has been studied recently in connection with the phenomenon of spectral pollution in …
Non-consistent approximations of self-adjoint eigenproblems: application to the supercell method
In this article, we introduce a general theoretical framework to analyze non-consistent
approximations of the discrete eigenmodes of a self-adjoint operator. We focus in particular …
approximations of the discrete eigenmodes of a self-adjoint operator. We focus in particular …
Spectral enclosure and superconvergence for eigenvalues in gaps
J Hinchcliffe, M Strauss - Integral Equations and Operator Theory, 2016 - Springer
We consider the problem of how to compute eigenvalues of a self-adjoint operator when a
direct application of the Galerkin (finite-section) method is unreliable. The last two decades …
direct application of the Galerkin (finite-section) method is unreliable. The last two decades …