FEAST Eigensolver for non-Hermitian Problems

TL;DR

The paper introduces an upgraded FEAST eigensolver capable of efficiently computing selected interior eigenvalues and eigenvectors for non-Hermitian problems, expanding its applicability and maintaining high performance.

Contribution

It presents a new version of the FEAST eigensolver tailored for non-Hermitian eigenproblems, with improved stability, usability, and parallelism.

Findings

Successfully computes interior eigenvalues in the complex plane.

Maintains convergence and parallelism of the original FEAST.

Enhances stability and usability for non-Hermitian problems.

Abstract

A detailed new upgrade of the FEAST eigensolver targeting non-Hermitian eigenvalue problems is presented and thoroughly discussed. It aims at broadening the class of eigenproblems that can be addressed within the framework of the FEAST algorithm. The algorithm is ideally suited for computing selected interior eigenvalues and their associated right/left bi-orthogonal eigenvectors,located within a subset of the complex plane. It combines subspace iteration with efficient contour integration techniques that approximate the left and right spectral projectors. We discuss the various algorithmic choices that have been made to improve the stability and usability of the new non-Hermitian eigensolver. The latter retains the convergence property and multi-level parallelism of Hermitian FEAST, making it a valuable new software tool for the scientific community.