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Nonlinear approximation from differentiable piecewise polynomials
 SIAM J. Math. Anal
"... piecewise polynomials ..."
Piecewisepolynomial regression trees
 Statistica Sinica
, 1994
"... A nonparametric function 1 estimation method called SUPPORT (“Smoothed and Unsmoothed PiecewisePolynomial 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 of the data ..."
Abstract

Cited by 51 (8 self)
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A nonparametric function 1 estimation method called SUPPORT (“Smoothed and Unsmoothed PiecewisePolynomial 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
POSITIVITY OF CONTINUOUS PIECEWISE POLYNOMIALS
"... Abstract. Real algebraic geometry provides certificates for the positivity of polynomials on semialgebraic sets by expressing them as a suitable combination of sums of squares and the defining inequalitites. We show how Putinar’s theorem for strictly positive polynomials on compact sets can be ap ..."
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be applied in the case of strictly positive piecewise polynomials on a simplicial complex. In the 1dimensional case, we improve this result to cover all nonnegative piecewise polynomials and give explicit degree bounds.
Feature Maps through Piecewise Polynomials
"... Efficient computation of channelcoded feature maps through piecewise polynomials ..."
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Efficient computation of channelcoded feature maps through piecewise polynomials
On the Dimension of Multivariate Piecewise Polynomials
 Longman Scientific and Technical
, 1986
"... 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 adj ..."
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Cited by 9 (1 self)
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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
Piecewise polynomials on polyhedral complexes
 ADVANCES IN APPLIED MATHEMATICS
, 2009
"... For a ddimensional 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 fo ..."
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Cited by 7 (3 self)
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For a ddimensional 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
Isometric Piecewise Polynomial Curves
, 1995
"... The main preoccupations of research in computeraided geometric design have been on shapespecification techniques for polynomial curves and surfaces, and on the continuity between segments or patches. When modelling with such techniques, curves and surfaces can be compressed or expanded arbitrarily. ..."
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Cited by 4 (0 self)
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. 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
Piecewise Polynomial Functions . . .
, 2006
"... 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 the co ..."
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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
The Dimension of the Space of C¹ Piecewise Polynomials
, 1996
"... 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 fourthdegree piecewise polynomials we define, inductively, a nodal basis on quite general meshes. ..."
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Cited by 1 (0 self)
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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 fourthdegree piecewise polynomials we define, inductively, a nodal basis on quite general meshes.
ON 3MONOTONE APPROXIMATION BY PIECEWISE POLYNOMIALS
"... Abstract. We consider 3monotone approximation by piecewise polynomials with prescribed knots. A general theorem is proved, which reduces the problem of 3monotone uniform approximation of a 3monotone function, to convex local L1 approximation of the derivative of the function. As the corollary we ..."
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Cited by 2 (0 self)
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Abstract. We consider 3monotone approximation by piecewise polynomials with prescribed knots. A general theorem is proved, which reduces the problem of 3monotone uniform approximation of a 3monotone function, to convex local L1 approximation of the derivative of the function. As the corollary
Results 1  10
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