Abstract
We propose two adaptations of linear Hermite subdivision schemes to operate on manifold-valued data. Our approach is based on a Log-exp analogue and on projection, respectively, and can be applied to both interpolatory and noninterpolatory Hermite schemes. Furthermore, we introduce a new proximity condition, which bounds the difference between a linear Hermite subdivision scheme and its manifold-valued analogue. Verification of this condition gives the main result: The manifold-valued Hermite subdivision scheme constructed from a C^1-convergent linear scheme is also C^1 if certain technical conditions are met.
Original language | English |
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Pages (from-to) | 3003-3031 |
Number of pages | 29 |
Journal | SIAM Journal on Numerical Analysis |
Volume | 54 |
Issue number | 5 |
DOIs | |
Publication status | Published - 4 Oct 2016 |
ASJC Scopus subject areas
- Numerical Analysis
Fields of Expertise
- Information, Communication & Computing