Vol. 9, No. 3, 2016

Download this article
Download this article For screen
For printing
Recent Issues

Volume 11, 1 issue

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
Cover Page
Editorial Board
Editors’ Addresses
Editors’ Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Ethics Statement
Subscriptions
Editorial Login
Author Index
Coming Soon
Contacts
 
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
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
Abstract

We study the ε-pseudospectra σε(A) of square matrices A N×N. We give a complete characterization of the ε-pseudospectra of 2×2 matrices and describe the asymptotic behavior (as ε 0) of σε(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