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1.
Francisco-Javier Muñoz-Delgado Victoriano Ramirez-González Paul Sablonnière 《分析论及其应用》1995,11(1):62-71
In this work we study linear polynomial operators preserving some consecutive i-convexities and leaving invariant the polynomials
up to a certain degree. First, we study the existence of an incom patibility between the conservation of certain i-convexities
and the invariance of a space of polynomials. Interpolation properties are obtained and a theorem by Berens and DeVore about
the Bernstein's operator is extended. Finally, from these results a generalized Bernstein's operator is obtained.
This work was supported by Junta de Andalucia. Grupo de investigación: Matemática Aplicada. Código: 1107 相似文献
2.
In this paper we generate and study new cubature formulas based on spline quasi-interpolants in the space of quadratic Powell-Sabin splines on nonuniform triangulations of a polygonal domain in ?2. By using a specific refinement of a generic triangulation, optimal convergence orders are obtained for some of these rules. Numerical tests are presented for illustrating the theoretical results. 相似文献
3.
Paul Sablonnière 《Numerical Algorithms》1992,2(3):241-254
Applying the generalized Euler transform to the firstn partial sums of a power series results in a triangular array whose inferior diagonal givesn approximate values of the sum of this series. The aim of this short note is to estimate the best of thesen values and to compare it with the actual best one for a collection of test series. 相似文献
4.
Abstract. We propose C
1
Hermite interpolants generated by the general subdivision scheme introduced by Merrien [17] and satisfying monotonicity
or convexity constraints. For arbitrary values and slopes of a given function f at the end-points of a bounded interval, which are compatible with the contraints, the given algorithms construct shape-preserving
interpolants. Moreover, these algorithms are quite simple and fast as well as adapted to CAGD. We also give error estimates
in the case of interpolation of smooth functions. 相似文献
5.
Let τ be some triangulation of a planar polygonal domain Ω. Given a smooth functionu, we construct piecewise polynomial functionsv∈C
ρ(Ω) of degreen=3 ρ for ρ odd, andn=3ρ+1 for ρ even on a subtriangulation τ3 of τ. The latter is obtained by subdividing eachT∈ρ into three triangles, andv/T is a composite triangular finite element, generalizing the classicalC
1 cubic Hsieh-Clough-Tocher (HCT) triangular scheme. The functionv interpolates the derivatives ofu up to order ρ at the vertices of τ. Polynomial degrees obtained in this way are minimal in the family of interpolation schemes
based on finite elements of this type. 相似文献
6.
In this paper we address the problem of constructing quasi-interpolants in the space of quadratic Powell-Sabin splines on
nonuniform triangulations. Quasi-interpolants of optimal approximation order are proposed and numerical tests are presented.
Dedicated to Prof. Mariano Gasca on the occasion of his 60th birthday. 相似文献
7.
8.
In this paper, we propose an interesting method for approximating the solution of a two dimensional second kind equation with a smooth kernel using a bivariate quadratic spline quasi-interpolant (abbr. QI) defined on a uniform criss-cross triangulation of a bounded rectangle. We study the approximation errors of this method together with its Sloan’s iterated version and we illustrate the theoretical results by some numerical examples. 相似文献
9.
Paul Sablonnière 《Advances in Computational Mathematics》2004,20(1-3):229-246
Bernstein bases, control polygons and corner-cutting algorithms are defined for C
1 Merrien's curves introduced in [7]. The convergence of these algorithms is proved for two specific families of curves. Results on monotone and convex interpolants which have been proved in [8] by Merrien and the author are also recovered. 相似文献
10.
Let be the triangulation generated by a uniform three direction mesh of the plane. Let
6 be the Powell-Sabin subtriangulation obtained by subdividing each triangleT by connecting each vertex to the midpoint of the opposite side.Given a smooth functionu, we construct a piecewise polynomial function C
r
(2) of degreen=2r (resp. 2r+1) forr odd (resp. even) in each triangle of
6, interpolating derivatives ofu up to orderr at the vertices of. 相似文献