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Piecewise polynomials on polyhedral complexes (2009)
| Venue: | ADVANCES IN APPLIED MATHEMATICS |
| Citations: | 7 - 3 self |
BibTeX
@INPROCEEDINGS{Mcdonald09piecewisepolynomials,
author = {Terry Mcdonald and Hal Schenck},
title = {Piecewise polynomials on polyhedral complexes},
booktitle = {ADVANCES IN APPLIED MATHEMATICS},
year = {2009},
pages = {82--93},
publisher = {}
}
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Abstract
For a d-dimensional polyhedral complex P, the dimension of the space of piecewise polynomial functions (splines) on P of smoothness r and degree k is given, for k sufficiently large, by a polynomial f(P,r,k) of degree d. When d = 2 and P is simplicial, in [1] Alfeld and Schumaker give a formula for all three coefficients of f. However, in the polyhedral case, no formula is known. Using localization techniques and specialized dual graphs associated to codimension–2 linear spaces, we obtain the first three coefficients of f(P,r,k), giving a complete answer when d = 2.
