Two-sided methods for the nonlinear eigenvalue problem

Abstract

We discuss solvers for the general nonlinear eigenvalue problem that are able to compute both left and right eigenvectors. A possible application is the approximation of the resolvent of a matrix-valued function. Our focus is on large-scale problems, in the context of SLEPc, the Scalable Library for Eigenvalue Problem Computations. We present two-sided variants of the NLEIGS and SLP methods. For the latter, we have implemented a nonequivalence deflation scheme. The accuracy and performance of the methods are analyzed for several problems coming from real applications.