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arXiv · 2402.18067

A gradient flow method for smooth splines versus least-squares fitting on Riemannian manifolds

Chun-Chi Lin·The Dung Tran
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Abstract

This article presents a novel resolution to the problem of spline interpolation versus least-squares fitting on smooth Riemannian manifolds utilizing the method of gradient flows of networks. This approach represents a contribution to both geometric control theory and statistical shape data analysis. Our work encompasses a rigorous proof for the existence of global solutions in H\"{o}lder spaces for the gradient flow. The asymptotic limits of these solutions establish the existence of the spline interpolation versus least-squares fitting problem on smooth Riemannian manifolds, offering a comprehensive solution. Notably, the constructive nature of the proof suggests potential numerical schemes for finding solutions.

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Chun-Chi Lin, The Dung Tran. 2024-02-28. A gradient flow method for smooth splines versus least-squares fitting on Riemannian manifolds. https://arxiv.org/abs/2402.18067

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