Convergence analysis of subdivision processes on the sphere

2020/01/26 by Hüning, Svenja, Wallner, Johannes
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2001.09426

Abstract

This paper provides a strategy to analyse the convergence of nonlinear analogues of linear subdivision processes on the sphere. In contrast to previous work, we study the Riemannian analogue of a linear scheme on a Riemannian manifold with positive sectional curvature. Our result can be applied to all general subdivision schemes without any sign restriction on the mask.

Related

• Convergence of subdivision schemes on Riemannian manifolds with nonpositive sectional curvature
• Convergence and normal continuity analysis of non-stationary subdivision schemes near extraordinary vertices and faces
• Analysis of a class of non linear subdivision schemes and associated multi-resolution transforms
• Smoothness of Nonlinear and Non-Separable Subdivision Schemes
• Subdivision Schemes in Metric Spaces