A New Highly Parallel Non-Hermitian Eigensolver
Abstract
Calculating portions of eigenvalues and eigenvectors of matrices or matrix pencils has many applications. An approach to this calculation for Hermitian problems based on a density matrix has been proposed in 2009 and a software package called FEAST has been developed. The density-matrix approach allows FEAST's implementation to exploit a key strength of modern computer architectures, namely, multiple levels of parallelism. Consequently, the software package has been well received and subsequently commercialized. A detailed theoretical analysis of Hermitian FEAST has also been established very recently. This paper generalizes the FEAST algorithm and theory, for the first time, to tackle non-Hermitian problems. Fundamentally, the new algorithm is basic subspace iteration or Bauer bi-iteration, except applied with a novel accelerator based on Cauchy integrals. The resulting algorithm retains the multi-level parallelism of Hermitian FEAST, making it a valuable new tool for large-scale computational science and engineering problems on leading-edge computing platforms.
Cite
@article{arxiv.1404.2891,
title = {A New Highly Parallel Non-Hermitian Eigensolver},
author = {Ping Tak Peter Tang and James Kestyn and Eric Polizzi},
journal= {arXiv preprint arXiv:1404.2891},
year = {2014}
}