Convergence analysis of subdivision processes on the sphere

Abstract We analyse the convergence of nonlinear Riemannian analogues of linear subdivision processes operating on data in the sphere. We show how for curve subdivision rules we can derive bounds guaranteeing convergence if the density of input data is below that threshold. Previous results only yie...

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Veröffentlicht in:IMA journal of numerical analysis 2022-01, Vol.42 (1), p.698-711
Hauptverfasser: Hüning, Svenja, Wallner, Johannes
Format: Artikel
Sprache:eng
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Zusammenfassung:Abstract We analyse the convergence of nonlinear Riemannian analogues of linear subdivision processes operating on data in the sphere. We show how for curve subdivision rules we can derive bounds guaranteeing convergence if the density of input data is below that threshold. Previous results only yield thresholds that are several magnitudes smaller and are thus useless for a priori checking of convergence. It is the first time that such a result has been shown for a geometry with positive curvature and for subdivision rules not enjoying any special properties like being interpolatory or having non-negative mask.
ISSN:0272-4979
1464-3642
DOI:10.1093/imanum/draa086