An efficient method for counting the eigenvalues inside a region in the complex plane

Guojian Yin

Published 2015-03-17Version 1

In many applications, the information about the number of eigenvalues inside a given region is required. In this paper, we propose a contour-integral based method for this purpose. The new method is motivated by two findings. Recently, some contour-integral based methods were developed for estimating the number of eigenvalues inside a region in the complex plane. But our method is able to count the eigenvalues inside the given region exactly. An appealing feature of our method is that it can integrate with recently developed contour-integral based eigensolvers to determine whether all desired eigenvalues are found by these methods. Numerical experiments are reported to show the viability of our new method.