Subdivision and Spline Spaces

A standard construction in approximation theory is mesh refinement. For a simplicial or polyhedral mesh Δ ⊆ R k , we study the subdivision Δ ′ obtained by subdividing a maximal cell of Δ . We give sufficient conditions for the module of splines on Δ ′ to split as the direct sum of splines on Δ and s...

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Bibliographic Details
Published in:Constructive approximation Vol. 47; no. 2; pp. 237 - 247
Main Authors: Schenck, Hal, Sorokina, Tatyana
Format: Journal Article
Language:English
Published: New York Springer US 01.04.2018
Springer Nature B.V
Subjects:
Analysis
Construction standards
Mathematics
Mathematics and Statistics
Numerical Analysis
Splines
Subdivisions
Subdivision
13D40
41A15
Spline
Dimension formula
ISSN:0176-4276, 1432-0940
Online Access:Get full text
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Summary:A standard construction in approximation theory is mesh refinement. For a simplicial or polyhedral mesh Δ ⊆ R k , we study the subdivision Δ ′ obtained by subdividing a maximal cell of Δ . We give sufficient conditions for the module of splines on Δ ′ to split as the direct sum of splines on Δ 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.
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ISSN:0176-4276
1432-0940
DOI:10.1007/s00365-017-9367-5