Complete Hermite–Birkhoff interpolation on scattered data by combined Shepard operators

Dell’Accio, Francesco; Tommaso, Filomena Di

doi:10.1016/j.cam.2015.12.016

Cited by 24 publications

(12 citation statements)

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“…This drawback can be avoided by considering various methods; for instance, it is possible to use partition of unity methods [24,25] or Shepard's like methods [26][27][28][29][30][31][32]. This problem can also be avoided by using B-spline quasi-interpolation.…”

Section: New Quasi-interpolation Methodsmentioning

confidence: 99%

A New Approximation Method with High Order Accuracy

Jiang

2017

MCA

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Abstract:In this paper, we propose a new multilevel univariate approximation method with high order accuracy using radial basis function interpolation and cubic B-spline quasi-interpolation. The proposed approach includes two schemes, which are based on radial basis function interpolation with less center points, and cubic B-spline quasi-interpolation operator. Error analysis shows that our method produces higher accuracy compared with other approaches. Numerical examples demonstrate that the proposed scheme is effective.

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Section: New Quasi-interpolation Methodsmentioning

confidence: 99%

A New Approximation Method with High Order Accuracy

Jiang

2017

MCA

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“…This approach turns out to be particularly meaningful when strongly non-uniform data-points are considered as in [3]. Moreover, further extensions could concern the parallel implementation of new schemes for Hermite-Birkhoff interpolation [12] and based on rescaled RBFs [13].…”

Section: Discussionmentioning

confidence: 99%

OpenCL Based Parallel Algorithm for RBF-PUM Interpolation

2017

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“…The latter are then used in combination with linear polynomials that locally interpolate the given data at the vertices of each triangle. Polynomials based on the vertices of a triangle [4,5,6] are used in combination with Shepard basis functions in [7,8,9,10]. To extend the point-based basis functions in (2) to triangle-based basis functions, let us consider a triangulation…”

Section: Shepard and Triangular Shepard Operatorsmentioning

confidence: 99%

On the enhancement of the approximation order of triangular Shepard method

Dell’Accio¹,

Tommaso²,

Hormann³

2016

AIP Conference Proceedings

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Shepard's method is a well-known technique for interpolating large sets of scattered data. The classical Shepard operator reconstructs an unknown function as a normalized blend of the function values at the scattered points, using the inverse distances to the scattered points as weight functions. Based on the general idea of defining interpolants by convex combinations, Little suggested to extend the bivariate Shepard operator in two ways. On the one hand, he considers a triangulation of the scattered points and substitutes function values with linear polynomials which locally interpolate the given data at the vertices of each triangle. On the other hand, he modifies the classical point-based weight functions and defines instead a normalized blend of the locally interpolating polynomials with triangle-based weight functions which depend on the product of inverse distances to the three vertices of the corresponding triangle. The resulting triangular Shepard operator interpolates all data required for its definition and reproduces polynomials up to degree 1, whereas the classical Shepard operator reproduces only constants, and has quadratic approximation order. In this paper we discuss an improvement of the triangular Shepard operator.

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Complete Hermite–Birkhoff interpolation on scattered data by combined Shepard operators

Cited by 24 publications

References 10 publications

A New Approximation Method with High Order Accuracy

A New Approximation Method with High Order Accuracy

OpenCL Based Parallel Algorithm for RBF-PUM Interpolation

On the enhancement of the approximation order of triangular Shepard method

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