Abstract

In many applications, the information about the number of eigenvalues inside a given region, rather than the eigenvalues, is required. In this talk, I will introduce a contour-integral based method for this purpose. Our method is motivated by two findings. There exist methods for estimation the number of eigenvalues inside a region in the complex plan, but our method is able to compute the number exactly. Our method has a good potential to be implemented on a high-performance parallel architecture. Numerical experiments will be reported to show the viability of our method.