Rate of Convergence of Hermite-Fejér Interpolation on the Unit Circle

Berriochoa, E.; Cachafeiro, A.; Díaz, J.; Martínez-Brey, E.

doi:10.1155/2013/407128

Cited by 6 publications

(2 citation statements)

References 8 publications

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“…Berriochoa, Cachafeiro and García-Amor [2] extended the Fejér's second theorem to the unit circle. Then Berriochoa, Cachafeiro, Díaz, and Martínez Brey [3] obtained the supremum norm of the error of interpolation for analytic functions and computed the order of convergence of Hermite-Fejér interpolation on the unit circle considering the same set of nodes as of [6].…”

Section: Introductionmentioning

confidence: 99%

Higher order Hermite-Fejer Interpolation on the unit circle

Bahadur¹,

Varun²

2022

Preprint

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The aim of this paper is to study the approximation of functions using a higher-order Hermite-Fejér interpolation process on the unit circle. The system of nodes is composed of vertically projected zeros of Jacobi polynomials onto the unit circle with boundary points at ±1. Values of the polynomial and its first four derivatives are fixed by the interpolation conditions at the nodes. Convergence of the process is obtained for analytic functions on a suitable domain, and the rate of convergence is estimated.

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Section: Introductionmentioning

confidence: 99%

Higher order Hermite-Fejer Interpolation on the unit circle

Bahadur¹,

Varun²

2022

Preprint

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“…Some improvements to this result, considering nonvanishing derivatives and more smooth functions, were given in [4]. More recently, in [5], the order of convergence of Hermite-Fejér interpolants for analytic functions on a disk and on an annulus containing the unit circle was obtained.…”

Section: Introductionmentioning

confidence: 99%

Hermite Interpolation on the Unit Circle Considering up to the Second Derivative

Berriochoa

Cachafeiro

Díaz

2014

ISRN Mathematical Analysis

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The paper is devoted to study the Hermite interpolation problem on the unit circle. The interpolation conditions prefix the values of the polynomial and its first two derivatives at the nodal points and the nodal system is constituted by complex numbers equally spaced on the unit circle. We solve the problem in the space of Laurent polynomials by giving two different expressions for the interpolation polynomial. The first one is given in terms of the natural basis of Laurent polynomials and the remarkable fact is that the coefficients can be computed in an easy and efficient way by means of the Fast Fourier Transform (FFT). The second expression is a barycentric formula, which is very suitable for computational purposes.

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On the asymptotic constant for the rate of Hermite–Fejér convergence on Chebyshev nodes

Berriochoa

Cachafeiro

2015

Acta Math. Hungar.

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Rate of Convergence of Hermite-Fejér Interpolation on the Unit Circle

Cited by 6 publications

References 8 publications

Higher order Hermite-Fejer Interpolation on the unit circle

Higher order Hermite-Fejer Interpolation on the unit circle

Hermite Interpolation on the Unit Circle Considering up to the Second Derivative

On the asymptotic constant for the rate of Hermite–Fejér convergence on Chebyshev nodes

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