Year: 2016
Type: preprint
Abstract: A standard construction in approximation theory is mesh refinement. For a simplicial or polyhedral mesh D in R^k, we study the subdivision D' obtained by subdividing a maximal cell of D. We give sufficient conditions for the module of splines on D' to split as the direct sum of splines on D and splines on the subdivided cell. As a consequence, we obtain dimension formulas and explicit bases for several commonly used subdivisions and their multivariate generalizations.
Source: arXiv (Cornell University)
Authors: Schenck, Hal, Sorokina, Tatyana
Institutions: University of Illinois Urbana-Champaign, Towson University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
Award: Systemic risk and topology
OpenAlex ID: W2953374956