Explicit bounds for the pseudospectra of various classes of matrices and operators

Gong, Feixue; Meyerson, Olivia; Meza, Jeremy; Stoiciu, Mihai; Ward, Abigail

doi:10.2140/involve.2016.9.517

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1944-4184 (online)

ISSN 1944-4176 (print)

Author index

To appear

Other MSP journals

Explicit bounds for the pseudospectra of various classes of matrices and operators

Feixue Gong, Olivia Meyerson, Jeremy Meza, Mihai Stoiciu and Abigail Ward

Vol. 9 (2016), No. 3, 517–540

DOI: 10.2140/involve.2016.9.517

Abstract

We study the $ε$ -pseudospectra $σ_{ε} (A)$ of square matrices $A \in ℂ^{N \times N}$ . We give a complete characterization of the $ε$ -pseudospectra of $2 \times 2$ matrices and describe the asymptotic behavior (as $ε \to 0$ ) of $σ_{ε} (A)$ for every square matrix $A$ . We also present explicit upper and lower bounds for the $ε$ -pseudospectra of bidiagonal matrices, as well as for finite-rank operators.

Keywords

spectrum, pseudospectrum, bidiagonal matrices, perturbation of eigenvalues

Mathematical Subject Classification 2010

Primary: 15A18, 15A60, 47A10, 65F15

Milestones

Received: 25 May 2015

Revised: 22 June 2015

Accepted: 23 June 2015

Published: 3 June 2016

Communicated by Stephan Garcia

Authors

Feixue Gong
Department of Mathematics and Statistics Williams College Williamstown, MA 01267 United States

Olivia Meyerson
Department of Mathematics and Statistics Williams College Williamstown, MA 01267 United States

Jeremy Meza
Department of Mathematics Carnegie Mellon University Pittsburgh, PA 15213 United States

Mihai Stoiciu
Department of Mathematics and Statistics Williams College Williamstown, MA 01267 United States

Abigail Ward
Department of Mathematics The University of Chicago Chicago, IL 60637 United States

Vol. 9, No. 3, 2016