Dissipative numerical schemes on Riemannian manifolds with applications to gradient flows
Journal article, Peer reviewed
Published version
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Date
2018Metadata
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- Institutt for matematiske fag [2527]
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Original version
10.1137/18M1190628Abstract
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: interferometric synthetic aperture radar denoising and diffusion tensor imaging denoising.