An Extension of Fejér’s Condition for Hermite Interpolation

Berriochoa, E.; Cachafeiro, A.; García-Amor, J.

doi:10.1007/s11785-011-0161-2

Cited by 6 publications

(5 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The left-hand side in Figure 3 shows the real part of the interpolator with the interpolated function near z = 1, the most problematic area. We obtained the interpolator by using the formula (11). We observed that they were indistinguishable.…”

Section: Mechanical Models and Numerical Examplesmentioning

confidence: 95%

“…In this case, the nodal system satisfies (13), and we can confidently use the interpolation methods. To compute the interpolation polynomials, we used the barycentric representation given by (11).…”

Section: Mechanical Models and Numerical Examplesmentioning

confidence: 99%

“…By using these nodal systems, the convergence of the Hermite-Fejér interpolation polynomials related to continuous functions was studied in [10], obtaining a Fejér-type theorem. The convergence of the Hermite interpolation polynomials taking nonvanishing conditions for the derivatives was studied in [11] giving several versions of the second Fejér-type theorem.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Mechanical Models for Hermite Interpolation on the Unit Circle

et al. 2021

Self Cite

View full text Add to dashboard Cite

In the present paper, we delve into the study of nodal systems on the unit circle that meet certain separation properties. Our aim was to study the Hermite interpolation process on the unit circle by using these nodal arrays. The target was to develop the corresponding interpolation theory in order to make practical use of these nodal systems linked to certain mechanical models that fit these distributions.

show abstract

Section: Mechanical Models and Numerical Examplesmentioning

confidence: 95%

Section: Mechanical Models and Numerical Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Mechanical Models for Hermite Interpolation on the Unit Circle

et al. 2021

Self Cite

View full text Add to dashboard Cite

show abstract

“…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

View full text Add to dashboard Cite

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.

show abstract

“…In [5] second Fejér's theorem concerning the Hermite interpolation with nonvanishing derivatives is extended, to the unit circle. New conditions for the derivatives are obtained in order that the Hermite interpolants uniformly converge to continuous functions on the unit circle.…”

Section: Introductionmentioning

confidence: 99%