A canonical form for the continuous piecewise polynomial functions

A canonical form for the continuous piecewise polynomial functions

We present in this paper a canonical form for the elements in the ring of continuous piecewise polynomial functions. This new representation is based on the use of a particular class of functions {Ci(P ) : P ∈ Q[x], i = 0, . . . , deg(P )} defined by Ci(P )(x) = { 0 if x ≤ α P (x) if x ≥ α where α is the i-th real root of the polynomial P . These functions will allow us to represent and manipul...

A canonical form for some piecewise defined functions

We define a canonical form for piecewise defined functions. We show that this has a wider range of application as well as better complexity properties than previous work.

Fitting piecewise linear continuous functions

We consider the problem of fitting a continuous piecewise linear function to a finite set of data points, modeled as a mathematical program with convex objective. We review some fitting problems that can be modeled as convex programs, and then introduce mixed-binary generalizations that allow variability in the regions defining the best-fit function’s domain. We also study the additional constr...

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 ...

Numerical Technique for the Convolution of Piecewise Polynomial Functions