A harmonic FEAST algorithm for non-Hermitian generalized eigenvalue problems

Abstract

The FEAST algorithm, a contour-integral based eigensolver, was developed for computing the eigenvalues inside a given interval, along with their eigenvectors, of a Hermitian generalized eigenproblem. The FEAST algorithm is a fast and stable technique, and is easily parallelizable. However, it was shown that this algorithm may fail to find the desired eigenpairs when applied to non-Hermitian problems. Efforts have been made to adapt FEAST to non-Hermitian problems. In this work, we aim at formulating a new non-Hermitian scheme for the FEAST algorithm. Our new scheme is based on the partial generalized Schur decomposition. Unlike the existing non-Hermitian FEAST methods, our method seeks approximation to the generalized Schur vectors instead of the potentially ill-conditioned eigenvectors. Our new method can compute not only the eigenvectors but also the right and left generalized Schur vectors corresponding to target eigenvalues. We present standard benchmark numerical experiments in which our method achieves better stability and efficiency comparing with the existing non-Hermitian FEAST algorithms.