scholarly journals Hermite interpolation by piecewise polynomial surfaces with polynomial area element

2017 ◽  
Vol 51 ◽  
pp. 30-47 ◽  
Author(s):  
Michal Bizzarri ◽  
Miroslav Lávička ◽  
Zbyněk Šír ◽  
Jan Vršek
Keyword(s):  
Hermite Interpolation ◽  
Piecewise Polynomial ◽  
Area Element

Basic circuit structures for the synthesis of piecewise polynomial one-port resistors

1985 ◽  
Vol 132 (4) ◽  
pp. 123 ◽  
Author(s):  
A. Rueda ◽  
J.L. Huertas ◽  
A. Rodriguez-Vazquez
Keyword(s):  
Piecewise Polynomial ◽  
Basic Circuit

scholarly journals On the Convexity Preservation of a Quasi C3 Nonlinear Interpolatory Reconstruction Operator on σ Quasi-Uniform Grids

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 310 ◽  
Author(s):  
Pedro Ortiz ◽  
Juan Carlos Trillo
Keyword(s):  
Initial Data ◽  
Numerical Experiments ◽  
Approximation Order ◽  
Piecewise Polynomial ◽  
Nonuniform Grids ◽  
Uniform Grids ◽  
Reconstruction Operator ◽  
Convexity Properties ◽  
Second Degree

This paper is devoted to introducing a nonlinear reconstruction operator, the piecewise polynomial harmonic (PPH), on nonuniform grids. We define this operator and we study its main properties, such as its reproduction of second-degree polynomials, approximation order, and conditions for convexity preservation. In particular, for σ quasi-uniform grids with σ≤4, we get a quasi C3 reconstruction that maintains the convexity properties of the initial data. We give some numerical experiments regarding the approximation order and the convexity preservation.

On the Hermite interpolation

2007 ◽  
Vol 50 (11) ◽  
pp. 1651-1660 ◽  
Author(s):  
Xing-hua Wang
Keyword(s):  
Hermite Interpolation

Algorithm 211: Hermite interpolation

1963 ◽  
Vol 6 (10) ◽  
pp. 617 ◽  
Author(s):  
George R. Schubert
Keyword(s):  
Hermite Interpolation

Multivariate piecewise polynomials

Acta Numerica ◽  
1993 ◽  
Vol 2 ◽  
pp. 65-109 ◽  
Author(s):  
C. de Boor
Keyword(s):  
Approximation Theory ◽  
Variational Approach ◽  
Polynomial Function ◽  
Piecewise Polynomial ◽  
Multivariate Splines ◽  
Piecewise Polynomial Function ◽  
Multivariate Spline ◽  
Piecewise Polynomials ◽  
The Subject ◽  
Function Of Several Arguments

This article was supposed to be on ‘multivariate splines». An informal survey, taken recently by asking various people in Approximation Theory what they consider to be a ‘multivariate spline’, resulted in the answer that a multivariate spline is a possibly smooth piecewise polynomial function of several arguments. In particular the potentially very useful thin-plate spline was thought to belong more to the subject of radial basis funtions than in the present article. This is all the more surprising to me since I am convinced that the variational approach to splines will play a much greater role in multivariate spline theory than it did or should have in the univariate theory. Still, as there is more than enough material for a survey of multivariate piecewise polynomials, this article is restricted to this topic, as is indicated by the (changed) title.

scholarly journals PIECEWISE POLYNOMIAL APPROXIMATIONS TO THE ICRP 116 EFFECTIVE DOSE COEFFICIENTS: PHOTONS AND NEUTRONS

2017 ◽  
Vol 178 (3) ◽  
pp. 310-321
Author(s):  
M M Mille ◽  
N E Hertel ◽  
P M Bergstrom ◽  
C Lee
Keyword(s):  
Effective Dose ◽  
Piecewise Polynomial ◽  
Polynomial Approximations ◽  
Dose Coefficients
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