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arXiv · 2404.04073

Newton's method for nonlinear mappings into vector bundles

Laura Weigl·Anton Schiela
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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.

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Laura Weigl, Anton Schiela. 2024-04-05. Newton's method for nonlinear mappings into vector bundles. https://arxiv.org/abs/2404.04073

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