Manifold-valued subdivision schemes based on geodesic inductive averaging

Nira Dyn; Nir Sharon

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arXiv · 1407.8361

Manifold-valued subdivision schemes based on geodesic inductive averaging

Nira Dyn·Nir Sharon

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Abstract

Subdivision schemes have become an important tool for approximation of manifold-valued functions. In this paper, we describe a construction of manifold-valued subdivision schemes for geodesically complete manifolds. Our construction is based upon the adaptation of linear subdivision schemes using the notion of repeated binary averaging, where as a repeated binary average we propose to use the geodesic inductive mean. We derive conditions on the adapted schemes which guarantee convergence from any initial manifold-valued sequence. The definition and analysis of convergence are intrinsic to the manifold. The adaptation technique and the convergence analysis are demonstrated by several important examples.

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Nira Dyn, Nir Sharon. 2014-07-31. Manifold-valued subdivision schemes based on geodesic inductive averaging. https://arxiv.org/abs/1407.8361

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