Localization of generalized eigenvalues by Cartesian ovals
Article first published online: 3 NOV 2011
Copyright © 2011 John Wiley & Sons, Ltd.
Numerical Linear Algebra with Applications
Volume 19, Issue 4, pages 728–741, August 2012
How to Cite
Kostić, V., Varga, R. S. and Cvetković, L. (2012), Localization of generalized eigenvalues by Cartesian ovals. Numer. Linear Algebra Appl., 19: 728–741. doi: 10.1002/nla.801
- Issue published online: 10 JUL 2012
- Article first published online: 3 NOV 2011
- Manuscript Accepted: 20 JUN 2011
- Manuscript Revised: 30 MAY 2011
- Manuscript Received: 1 MAY 2010
- Geršgorin sets;
- generalized eigenvalues;
In this paper, we consider the localization of generalized eigenvalues, and we discuss ways in which the Gersgorin set for generalized eigenvalues can be approximated. Earlier, Stewart proposed an approximation using a chordal metric. We will obtain here an improved approximation, and using the concept of generalized diagonal dominance, we prove that the new approximation has some of the basic properties of the original Geršgorin set, which makes it a handy tool for generalized eigenvalue localization. In addition, an isolation property is proved for both the generalized Geršgorin set and its approximation. Copyright © 2011 John Wiley & Sons, Ltd.