Regularity of Mixed Spline Spaces [article]

Michael DiPasquale
2014 arXiv   pre-print
We derive bounds on the regularity of the algebra C^α(P) of mixed splines over a central polytopal complex P⊂R^3. As a consequence we bound the largest integer d (the postulation number) for which the Hilbert polynomial HP(C^α(P),d) disagrees with the Hilbert function HF(C^α(P),d)= C^α(P)_d. The polynomial HP(C^α(P),d) has been computed in [DiPasquale 2014], building on [McDonald-Schenck 09] and [Geramita-Schenck 98]. Hence the regularity bounds obtained indicate when a known polynomial gives
more » ... e correct dimension of the spline space C^α(P)_d. In the simplicial case with all smoothness parameters equal, we recover a bound originally due to [Hong 91] and [Ibrahim and Schumaker 91].
arXiv:1411.2176v1 fatcat:bycrat34dzff5e5jag5a652yte