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arXiv · 1804.08104

Dissipative numerical schemes on Riemannian manifolds with applications to gradient flows

Elena Celledoni·Sølve Eidnes·Brynjulf Owren·Torbjørn Ringholm
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Abstract

This paper concerns an extension of discrete gradient methods to finite-dimensional Riemannian manifolds termed discrete Riemannian gradients, and their application to dissipative ordinary differential equations. This includes Riemannian gradient flow systems which occur naturally in optimization problems. The Itoh--Abe discrete gradient is formulated and applied to gradient systems, yielding a derivative-free optimization algorithm. The algorithm is tested on two eigenvalue problems and two problems from manifold valued imaging: InSAR denoising and DTI denoising.

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Elena Celledoni, Sølve Eidnes, Brynjulf Owren, Torbjørn Ringholm. 2018-04-22. Dissipative numerical schemes on Riemannian manifolds with applications to gradient flows. https://arxiv.org/abs/1804.08104

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