Localization of generalized eigenvalues by Cartesian ovals


V. Kostić, Department of Mathematics and Informatics, Faculty of Science, University of Novi Sad, Novi Sad, Serbia.

E-mail: vkostic@dmi.uns.ac.rs


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.