Saved in:
Bibliographic Details
Main Authors: Weigl, Laura, Schiela, Anton
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2404.04073
Tags: Add Tag
No Tags, Be the first to tag this record!
Table of Contents:
  • We consider Newton's method for finding zeros of mappings from a manifold $\mathcal X$ into a vector bundle $\mathcal E$. In this setting a connection on $\mathcal E$ is required to render the Newton equation well defined, and a retraction on $\mathcal X$ is needed to compute a Newton update. We discuss local convergence in terms of suitable differentiability concepts, using a Banach space variant of a Riemannian distance. We also carry over an affine covariant damping strategy to our setting. Finally, we will illustrate our results by applying them to generalized non-symmetric eigenvalue problems and providing a numerical example.