An Iterative Method for Contour-Based Nonlinear Eigensolvers
Abstract
Contour integration techniques have become a popular choice for solving the linear and non-linear eigenvalue problems. They principally include the Sakurai-Sugiura methods, the Beyn's algorithm, the FEAST/NLFEAST algorithms and other rational filtering techniques. While these methods can result in effective 'black-box' approach for solving linear eigenvalue problems, they still present several shortcomings for addressing nonlinear eigenvalue problems which are both mathematically and practically far more challenging. In this paper, we introduce a new hybrid algorithm that advantageously combines the iterative nature of NLFEAST with the effectiveness of Beyn's approach to deal with general non-linearity. In doing so, this NLFEAST-Beyn hybrid algorithm can overcome current limitations of both algorithms taken separately. After presenting its derivation from both a Beyn's and NLFEAST's perspective, several numerical examples are discussed to demonstrate the efficiency of the new technique.
Cite
@article{arxiv.2007.03000,
title = {An Iterative Method for Contour-Based Nonlinear Eigensolvers},
author = {Julien Brenneck and Eric Polizzi},
journal= {arXiv preprint arXiv:2007.03000},
year = {2020}
}