A new numerical scheme for constrained total variation flows and its convergence

Giga, Yoshikazu; Sakakibara, Koya; Taguchi, Kazutoshi et al.

Hokkaido University Preprint Series in Mathematics, 2019, 1124, 1-33

Permalink : https://doi.org/10.14943/87742

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アクセス権	open access
DOI	https://doi.org/10.14943/87742
URI	https://hdl.handle.net/2115/73372
タイトル	A new numerical scheme for constrained total variation flows and its convergence
著者	Giga, Yoshikazu ; Sakakibara, Koya ; Taguchi, Kazutoshi ; Uesaka, Masaaki
著者名 Giga, Yoshikazu
著者名 Sakakibara, Koya
著者名 Taguchi, Kazutoshi
著者名 Uesaka, Masaaki
言語	英語
発行日	2019-04-01
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	1124
ページ	1-33
抄録	In this paper, we propose a new numerical scheme for a spatially discrete model of constrained total variation flows, which are total variation flows whose values are constrained in a Riemannian manifold. The difficulty of this problem is that the underlying function space is not convex and it is hard to calculate the minimizer of the functional with the manifold constraint. We overcome this difficulty by “localization technique" using the exponential map and prove the finite-time error estimate in general situation. Finally, we show a few numerical results for the cases that the target manifolds are S2 and SO(3).
資源タイプ	紀要論文
出版タイプ	Version of Record