A Newton method for solving locally definite multiparameter eigenvalue problems by multiindex
Numerical Analysis
2025-01-20 v2 Numerical Analysis
Abstract
We present a new approach to compute eigenvalues and eigenvectors of locally definite multiparameter eigenvalue problems by its signed multiindex. The method has the interpretation of a semismooth Newton method applied to certain functions that have a unique zero. We can therefore show local quadratic convergence, and for certain extreme eigenvalues even global linear convergence of the method. Local definiteness is a weaker condition than right and left definiteness, which is often considered for multiparameter eigenvalue problems. These conditions are naturally satisfied for multiparameter Sturm-Liouville problems that arise when separation of variables can be applied to multidimensional boundary eigenvalue problems.
Cite
@article{arxiv.2404.04194,
title = {A Newton method for solving locally definite multiparameter eigenvalue problems by multiindex},
author = {Henrik Eisenmann},
journal= {arXiv preprint arXiv:2404.04194},
year = {2025}
}