Piecewise polynomials on polyhedral complexes

Details Piecewise polynomials on polyhedral complexes Piecewise polynomials on polyhedral complexes

2008-08-14

arxiv.org/abs/0808.2031v1

Advances in Applied Mathematics, 42 (2009), 82-93

Mathematics

Commutative Algebra

12 pages, 7 figures

Scientific paper

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, Alfeld and Schumaker determined 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.

Affiliated with

Also associated with

No associations

Rating

Piecewise polynomials on polyhedral complexes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Piecewise polynomials on polyhedral complexes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Piecewise polynomials on polyhedral complexes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-584871