The evolution of piecewise polynomial wave functions

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...

Numerical Technique for the Convolution of Piecewise Polynomial Functions

Generalization of the Piecewise Polynomial Interpolation by Fractal Functions

The fractal interpolation functions defined by iterated function systems provide new methods of approximation and quantification of experimental data. The polynomial fractal functions can be considered as generalization of the piecewise polynomial interpolants. Assuming some hypotheses on the original function, a bound of the representation of the error for this kind of approximants is obtained...

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 ...

Piecewise Polynomial Functions and the Fast Fourier Transform

Piecewise polynomial functions are frequently used to approximate functions that exhibit complex behavior across a variety of scales. We investigate the use of nonuniform FFT (NUFFT) approaches to quickly and accurately evaluate the first several Fourier series coefficents of piecewise linear functions, and propose a new NUFFT approach that provides quick convergence at relatively low cost.