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Dissipative numerical schemes on Riemannian manifolds with applications to gradient flows

Celledoni, Elena; Eidnes, Sølve; Owren, Brynjulf; Ringholm, Torbjørn
Journal article, Peer reviewed
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URI
http://hdl.handle.net/11250/2581723
Date
2018
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  • Institutt for matematiske fag [1396]
  • Publikasjoner fra CRIStin - NTNU [19849]
Original version
10.1137/18M1190628
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: interferometric synthetic aperture radar denoising and diffusion tensor imaging denoising.
Publisher
Society for Industrial and Applied Mathematics
Journal
SIAM Journal on Scientific Computing

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