I have a generalized eigen-problem: $A\psi = \lambda B \psi$ with $A$ and $B$ are large (>1000) complex non-Hermitian matrices. I know that eigenvalues with largest and smallest absolute values can be found using iterative approaches like ARPACK. But I am only interested in those complex eigenvalues (not all of them) with absolute values closest to 1. It there any fast and parallel approach to do this?
Eigenvalues with absolute values close to 1
linear algebra