English

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.

Keywords

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}
}
R2 v1 2026-06-28T13:23:05.778Z