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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Vydáno v:Constructive approximation Ročník 47; číslo 2; s. 237 - 247
Hlavní autoři: Schenck, Hal, Sorokina, Tatyana
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.04.2018
Springer Nature B.V
Témata:
Analysis
Construction standards
Mathematics
Mathematics and Statistics
Numerical Analysis
Splines
Subdivisions
Subdivision
13D40
41A15
Spline
Dimension formula
ISSN:0176-4276, 1432-0940
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Popis
Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0176-4276
1432-0940
DOI:10.1007/s00365-017-9367-5