Abstract
The paper deals with the order of convergence of the Laurent polynomials of Hermite-Fejér interpolation on the unit circle with nodal system, thenroots of a complex number with modulus one. The supremum norm of the error of interpolation is obtained for analytic functions as well as the corresponding asymptotic constants.
Highlights
The paper is devoted to study the Hermite-Fejer interpolation problem on the unit circle T
It is well known that it ensures uniform convergence of Hermite-Fejer interpolants to continuous functions on [−1, 1] taking as nodal system the Chebyshev points
In [1] the authors consider the nodal system of the n roots of a complex number with modulus one
Summary
The paper is devoted to study the Hermite-Fejer interpolation problem on the unit circle T. It is proved that the Laurent polynomials of Hermite-Fejer interpolation for a given continuous function f on the unit circle uniformly converge to f. An algorithm for efficient computing of the coefficients of the Laurent polynomials of Hermite-Fejer and Hermite interpolation with spaced nodes on the unit circle was given in [6] These results were extended to the bounded interval, and the corresponding expressions can be evaluated using the techniques given in [7]. The convergence of the Laurent polynomials of Hermite-Fejer interpolation has been studied in [8] for analytic functions defined on open sets containing the unit disk. The last section is devoted to some numerical experiments to reveal the contributions of our results
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