Extending piecewise polynomial functions in two variables

Extending Piecewise Polynomial Functions in Two Variables

We study the extensibility of piecewise polynomial functions defined on closed subsets of R2 to all of R2. The compact subsets of R2 on which every piecewise polynomial function is extensible to R2 can be characterized in terms of local quasi-convexity if they are definable in an o-minimal expansion of R. Even the noncompact closed definable subsets can be characterized if semialgebraic functio...

Piecewise Polynomial Functions on a Planar Region: Iii Abstract Piecewise Polynomial Functions on a Planar Region: Boundary Constraints And

Piecewise Polynomial Functions on a Planar Region: Boundary Constraints and Polyhedral Subdivisions. (May 2006) Terry Lynn McDonald, B.S., The University of Texas at Tyler; M.S., Texas A&M University Chair of Advisory Committee: Dr. Henry Schenck Splines are piecewise polynomial functions of a given order of smoothness r on a triangulated region ∆ (or polyhedrally subdivided region ) of R. The ...

Extending Means of Two Variables to Several Variables

We present a method, based on series expansions and symmetric polynomials, by which a mean of two variables can be extended to several variables. We apply it mainly to the logarithmic mean.

Numerical Technique for the Convolution of Piecewise Polynomial Functions

Fat Points, Inverse Systems, and Piecewise Polynomial Functions

We explore the connection between ideals of fat points (which correspond to subschemes of Pn obtained by intersecting (mixed) powers of ideals of points), and piecewise polynomial functions (splines) on a d-dimensional simplicial complex ∆ embedded in R. Using the inverse system approach introduced by Macaulay [11], we give a complete characterization of the free resolutions possible for ideals...