piecewise polynomials

A nonparametric function 1 estimation method called SUPPORT (“Smoothed and Unsmoothed Piecewise-Polynomial Regression Trees”) is described. The estimate is typically made up of several pieces, each piece being obtained by fitting a polynomial regression to the observations in a subregion

be applied in the case of strictly positive piecewise polynomials on a simplicial complex. In the 1-dimensional case, we improve this result to cover all non-negative piecewise polynomials and give explicit degree bounds.

Efficient computation of channel-coded feature maps through piecewise polynomials

Lower bounds are given on the dimension of piecewise polynomial C 1 and C 2 functions defined on a tessellation of a polyhedral domain into Tetrahedra. The analysis technique consists of embedding the space of interest into a larger space with a simpler structure, and then making appropriate

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

. There has been relatively little work on interacting with direct spatial properties of curves and surfaces, such as their arc length or surface area. As a first step, we derive families of parametric piecewise polynomial curves that satisfy various positional and tangential constraints together with arc

Splines are piecewise polynomial functions of a given order of smoothness r on a triangulated region ∆ (or polyhedrally subdivided region �) of R d. The set of splines of degree at most k forms a vector space C r k (∆). Moreover, a nice way to study C r k (∆) is to embed ∆ in Rd+1, and form

We present a method for computing the dimension of C¹ piecewise polynomials on a triangulated polygonal domain in the plane. Our results verify a conjecture of Strang in a large number of cases. For fourth-degree piecewise polynomials we define, inductively, a nodal basis on quite general meshes.

Abstract. We consider 3-monotone approximation by piecewise polynomials with pre-scribed knots. A general theorem is proved, which reduces the problem of 3-monotone uniform approximation of a 3-monotone function, to convex local L1 approximation of the derivative of the function. As the corollary