A Lower Bound for Splines on Tetrahedral Vertex Stars
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Publication:5001669
DOI10.1137/20M1341118zbMath1484.13036arXiv2005.13043OpenAlexW3172209357MaRDI QIDQ5001669
Nelly Villamizar, Michael Robert DiPasquale
Publication date: 23 July 2021
Published in: SIAM Journal on Applied Algebra and Geometry (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2005.13043
Numerical computation using splines (65D07) Spline approximation (41A15) Syzygies, resolutions, complexes and commutative rings (13D02) Divisors, linear systems, invertible sheaves (14C20)
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Cites Work
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- Bounds on the dimension of trivariate spline spaces: a homological approach
- Combinatorial bounds on Hilbert functions of fat points in projective space
- Bounds on the dimension of spaces of multivariate piecewise polynomials
- The dimension of bivariate spline spaces of smoothness r for degree \(d\geq 4r+1\)
- Super spline spaces of smoothness \(r\) and degree \(d\geq{} 3r+2\)
- Fat points, inverse systems, and piecewise polynomial functions
- Local cohomology of bivariate splines
- A family of ideals of minimal regularity and the Hilbert series of \(C^r(\widehat\Delta)\)
- A spectral sequence for splines
- Cohomology vanishing and a problem in approximation theory
- Algebraic methods in approximation theory
- Dimension of trivariate \(C^1\) splines on bipyramid cells
- Inverse system of a symbolic power. I
- On the dimension of bivariate spline spaces of smoothness r and degree \(d=3r+1\)
- A dimension series for multivariate splines
- A counter-example to the Schenck-Stiller ``\(2r + 1\) conjecture
- Piecewise polynomials on polyhedral complexes
- Splines on the Alfeld split of a simplex and type A root systems
- Are symbolic powers highly evolved?
- Lower Bound on the Dimension of Trivariate Splines on Cells
- Comparing powers and symbolic powers of ideals
- Spline Functions on Triangulations
- The Generic Dimension of the Space of $C^1$ Splines of Degree $d \geq 8$ on Tetrahedral Decompositions
- Lectures on Polytopes
- Dimension of mixed splines on polytopal cells
- Isogeometric Analysis
- Piecewise polynomials and the finite element method
- Dimension and Local Bases of Homogeneous Spline Spaces
- Homology of Smooth Splines: Generic Triangulations and a Conjecture of Strang
