An inexact Matrix-Newton method for solving NEPv
Numerical Analysis
2024-09-04 v2 Numerical Analysis
Abstract
In this paper, an inexact Newton method for solving real-valued nonlinear eigenvalue problems with eigenvector dependency (NEPv) is introduced that is able to solve the problem on a matrix level. Our main contribution is to derive a variant of Newton's method that uses global Krylov methods such as global GMRES to solve the linear operator equation necessary to compute the Newton correction in a matrix-free way. The advantages that this second order method has over the well-established SCF algorithm are explained and visualized by a variety of numerical experiments.
Cite
@article{arxiv.2311.09670,
title = {An inexact Matrix-Newton method for solving NEPv},
author = {Tom Werner},
journal= {arXiv preprint arXiv:2311.09670},
year = {2024}
}