ERef Bayreuth

Literature by the same author

at Google Scholar

Bibliografische Daten exportieren

Newton's method for nonlinear mappings into vector bundles

Title data

Weigl, Laura ; Schiela, Anton:
Newton's method for nonlinear mappings into vector bundles.
Bayreuth , 2024 . - 31 p.
DOI: https://doi.org/10.48550/arXiv.2404.04073

This is the latest version of this item.

Official URL:

Abstract in another language

We consider Newton's method for finding zeros of mappings from a manifold X into a vector bundle E. In this setting a connection on E is required to render the Newton equation well defined, and a retraction on 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 discuss some applications of our approach, namely, finding fixed points of vector fields, variational problems on manifolds and finding critical points of functionals.

Further data

Item Type:	Preprint, postprint
Refereed:	Yes
Keywords:	Newton’s method; Banach manifolds; vector bundles
Subject classification:	MSC classes: 53-08, 58C15, 46T05, 49M15
Institutions of the University:	Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics > Chair Applied Mathematics - Univ.-Prof. Dr. Anton Schiela Profile Fields Profile Fields > Advanced Fields Profile Fields > Advanced Fields > Nonlinear Dynamics
Result of work at the UBT:	Yes
DDC Subjects:	500 Science > 510 Mathematics
Date Deposited:	20 Jun 2024 08:25
Last Modified:	20 Jun 2024 08:25
URI:	https://eref.uni-bayreuth.de/id/eprint/89799

Available Versions of this Item

Newton's method for nonlinear mappings into vector bundles. (deposited 19 Apr 2024 07:28)
- Newton's method for nonlinear mappings into vector bundles. (deposited 20 Jun 2024 08:25) [Currently Displayed]