Abstract
Dimensions of spaces of multivariate splines remain unknown in general. A computational method to obtain explicit formulas for the dimension of spline spaces on simplicial partitions is described. The method is based on Hilbert series and Hilbert polynomials. It is applied to conjecture the dimension formulas for splines on the Alfeld split of a simplex and on several other partitions.
Acknowledgements
We thank Peter Alfeld for the essential computational tools he created and for the enlightening thoughts he shared with us.
Citation
Simon Foucart. Tatyana Sorokina. "GENERATING DIMENSION FORMULAS FOR MULTIVARIATE SPLINES." Albanian J. Math. 7 (1) 25 - 35, 2013. https://doi.org/10.51286/albjm/1364666232
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