Year: 2024
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Weigl, Laura, Schiela, Anton
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4394592005