An iterative approach to barycentric rational Hermite interpolation

Cirillo, Emiliano; Hormann, Kai

doi:10.1007/s00211-018-0986-y

Cited by 10 publications

(6 citation statements)

References 10 publications

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“…Cirillo and Hormann [3] show that these interpolants can be extended to the Hermite setting by letting…”

Section: Iterative Barycentric Rational Hermite Interpolationmentioning

confidence: 99%

“…In this paper we show that this favourable behaviour also holds for a generalization of these interpolants to the Hermite setting. After reviewing Cirillo and Hormann's [3] iterative construction of barycentric rational Hermite interpolants (Section 2), we show that for the special case of Floater-Hormann Hermite interpolation both Ω 0,n and Ω 1,n can be bounded from above by a constant that grows exponentially with d (Section 3). We conclude with some numerical examples that confirm this result (Section 4).…”

Section: Introductionmentioning

confidence: 99%

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On the Lebesgue constant of barycentric rational Hermite interpolants at equidistant nodes

Cirillo

Hormann

2019

Journal of Computational and Applied Mathematics

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Barycentric rational Floater-Hormann interpolants compare favourably to classical polynomial interpolants in the case of equidistant nodes, because the Lebesgue constant associated with these interpolants grows logarithmically in this setting, in contrast to the exponential growth experienced by polynomials. In the Hermite setting, in which also the first derivatives of the interpolant are prescribed at the nodes, the same exponential growth has been proven for polynomial interpolants, and the main goal of this paper is to show that much better results can be obtained with a recent generalization of Floater-Hormann interpolants. After summarizing the construction of these barycentric rational Hermite interpolants, we study the behaviour of the corresponding Lebesgue constant and prove that it is bounded from above by a constant. Several numerical examples confirm this result.

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“…Cirillo and Hormann [3] show that these interpolants can be extended to the Hermite setting by letting…”

Section: Iterative Barycentric Rational Hermite Interpolationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the Lebesgue constant of barycentric rational Hermite interpolants at equidistant nodes

Cirillo

Hormann

2019

Journal of Computational and Applied Mathematics

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“…A quadratic spline is composed of piecewise quadratic polynomials with continuous first-order derivatives at spline knots. In order to write its interpolation function according to interpolation data nodes directly, we create the above formula referring to the thought of barycentric rational Hermite interpolation [30]. Here we elaborate how we educe the formula above.…”

Section: Spline Interpolation Of Degree 0 1 Andmentioning

confidence: 99%

“…But for the quadratic spline, we also need to restrict the derivative at x i , so that the first-order derivative of the whole function at x i is continuous. Referring to the Hermite interpolation [30], we can think out the following expression:…”

Section: Spline Interpolation Of Degree 0 1 Andmentioning

confidence: 99%

Golden interpolation

He,

Chang

2018

Preprint

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For the classic aesthetic interpolation problem, we propose an entirely new thought: apply the golden section. For how to apply the golden section to interpolation methods, we present three examples: the golden step interpolation, the golden piecewise linear interpolation and the golden curve interpolation, which respectively deal with the applications of golden section in the interpolation of degree 0, 1, and 2 in the plane. In each example, we present our basic ideas, the specific methods, comparative examples and applications, and relevant criteria. And it is worth mentioning that for aesthetics, we propose two novel concepts: the golden cuspidal hill and the golden domed hill. This paper aims to provide the reference for the combination of golden section and interpolation, and stimulate more and better related researches.

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“…Another interesting barycentric rational trigonometric interpolant has been introduced in [2] and include Berrut's interpolant at equidistant nodes as a special case. Cirillo and Hormann in [6] presented an effective method to construct an Hermite interpolant starting from the basis b i (x) of the renowned Floater-Hormann family of interpolants, in fact they considered the basis…”

Section: Introductionmentioning

confidence: 99%

A barycentric trigonometric Hermite interpolant via an iterative approach

Elefante¹

2022

Preprint

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In this paper an interative approach for constructing the Hermite interpolant introduced by Cirillo and Hormann (2018) for the Floater-Hormann family of interpolants is extended and generalised. In particular, we apply that scheme to produce an effective barycentric rational trigonometric Hermite interpolant using the basis function of the interpolant introduced by Berrut (1988). In order to give an easy construction of such an interpolant we compute the differentation matrix analytically and we conclude with various examples and a numerical study of the rate of convergence at equidistant nodes.

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An iterative approach to barycentric rational Hermite interpolation

Cited by 10 publications

References 10 publications

On the Lebesgue constant of barycentric rational Hermite interpolants at equidistant nodes

On the Lebesgue constant of barycentric rational Hermite interpolants at equidistant nodes

Golden interpolation

A barycentric trigonometric Hermite interpolant via an iterative approach

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