Quasi-interpolation projectors for box splines

Lyche, Tom; Manni, Carla; Sablonnière, Paul

doi:10.1016/j.cam.2007.10.029

Cited by 19 publications

(11 citation statements)

References 17 publications

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“…i,j and Z (5) i,j are the middle points of Z (1) i,j Z (6) i,j and Z (3) i,j Z (6) i,j (see Fig. 3), respectively, for 1 ≤ i ≤ n and j = 1, 2, 3, then we have …”

Section: Now We Give Some Examples For Various Choices Of Zmentioning

confidence: 99%

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Construction of spherical spline quasi-interpolants based on blossoming

Ibáñez

Lamnii²,

Mraoui³

et al. 2010

Journal of Computational and Applied Mathematics

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a b s t r a c tA general theory of quasi-interpolants based on quadratic spherical Powell-Sabin splines on spherical triangulations of a sphere-like surface S is developed by using polar forms.As application, various families of discrete and differential quasi-interpolants reproducing quadratic spherical Bézier-Bernstein polynomials or the whole space of the spherical Powell-Sabin quadratic splines of class C 1 are presented.

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“…i,j and Z (5) i,j are the middle points of Z (1) i,j Z (6) i,j and Z (3) i,j Z (6) i,j (see Fig. 3), respectively, for 1 ≤ i ≤ n and j = 1, 2, 3, then we have …”

Section: Now We Give Some Examples For Various Choices Of Zmentioning

confidence: 99%

“…To ensure good approximation properties, it is important that the methods reproduce polynomials or the functions in the given spline space. Quasi-interpolatory operators have been extensively studied in several papers; see, for instance, [4][5][6][7][8][9] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Construction of spherical spline quasi-interpolants based on blossoming

Ibáñez

Lamnii²,

Mraoui³

et al. 2010

Journal of Computational and Applied Mathematics

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“…This yields the local approximation order characterized by the Strang-Fix conditions. The quasi-interpolants constructed in [22] reproduce not only polynomials, but also the whole spline space. Multivariate quasi-interpolation formulas are developed in [6].…”

Section: Introductionmentioning

confidence: 99%

“…We prove that the sparse B-spline quasi-interpolation which Quasi-interpolation has been widely studied in the field of approximation theory and its applications (see, [10][11][12][5][6][7][8][9]22,[28][29][30]). In particular, B-spline quasi-interpolation is used in [10] as a key tool to establish elementary facts about polynomial splines.…”

Section: Introductionmentioning

confidence: 99%

B-spline quasi-interpolation on sparse grids

Jiang

2011

Journal of Complexity

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a b s t r a c tWe propose a periodic B-spline quasi-interpolation for multivariate functions on sparse grids and develop a fast scheme for the evaluation of a linear combination of B-splines on sparse grids.We prove that both of these operations require only O(n log d−1 n) number of multiplications, where n is the number of univariate Bspline basis functions used in each coordinate direction and d is the number of variables of the functions. We also establish the optimal approximation order of the periodic B-spline quasi-interpolation. Numerical examples are presented to confirm the theoretical estimates.

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“…Based on the latter, we chose to use Box-splines, as the results are more stable. And lastly, also based on the previously cited paper, we decided to use a quasi-interpolation method [26].…”

Section: Box-splines Quasi-interpolationmentioning

confidence: 99%

Solving the guiding-center model on a regular hexagonal mesh

et al. 2016

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Abstract. This paper introduces a Semi-Lagrangian solver for the Vlasov-Poisson equations on a uniform hexagonal mesh. The latter is composed of equilateral triangles, thus it doesn't contain any singularities, unlike polar meshes. We focus on the guiding-center model, for which we need to develop a Poisson solver for the hexagonal mesh in addition to the Vlasov solver. For the interpolation step of the Semi-Lagrangian scheme, a comparison is made between the use of Box-splines and of Hermite finite elements. The code will be adapted to more complex models and geometries in the future. Résumé. Dans cet article nous présentons un solveur semi-Lagrangien pour leséquations de Vlasov-Poisson sur un maillage hexagonal uniforme. Ce dernier est composé de triangleséquilatéraux, ainsi il ne présente aucune singularité, contrairement au maillage polaire. Nous nous concentrons ici sur le modèle centre-guide.À cette fin nous avons développé en plus du solveur pour Vlasov, un solveur de l'équation de Poisson pour maillage hexagonal. Nous comparons les résultats obtenus avec une interpolation paréléments finis d'Hermite et par des Box-splines. Dans l'avenir, ce code sera adaptéà des géométries et modèles plus complexes.

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Quasi-interpolation projectors for box splines

Abstract: Special Issue: Recent Progress in Spline and Wavelet ApproximationInternational audienceWe consider box spline quasi-interpolants based on local linear functionals of point evaluator and integral type. The approximations are easy to compute, and reproduce the whole spline space in questio

Cited by 19 publications

References 17 publications

Construction of spherical spline quasi-interpolants based on blossoming

Construction of spherical spline quasi-interpolants based on blossoming

B-spline quasi-interpolation on sparse grids

Solving the guiding-center model on a regular hexagonal mesh

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