Title: Reliable computation of exterior eigenvalues through matrix functions

Abstract: Exterior eigenvalues of large sparse matrices are needed for

various applications, such as linear stability analysis. These

eigenvalues are difficult to compute efficiently and reliably if they

are much smaller than the dominant eigenvalues in modulus. Traditional

spectral transformations such as Cayley transform are far from reliable.

In this talk, we discuss a simple idea of spectral transformation based

on functions of matrices that maps the desired exterior eigenvalues to

dominant ones. Approximations of the action of matrix functions on

vectors is fundamental for this approach, which can be performed by

rational Krylov subspace methods (RKSM). Numerical experiments for

linear and nonlinear eigenvalue problems demonstrate the reliability of

this method.