HIGHER ORDER HERMITE-FEJER INTERPOLATION ON THE UNIT CIRCLE

HIGHER ORDER HERMITE-FEJER INTERPOLATION ON THE UNIT CIRCLE

S. Bahadur, Varun

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Abstract

The aim of this paper is to study the approximation of functions using a higher-order Hermite-Fej er 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  rst four derivatives are  xed 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.

Keywords

Unit circle, Non-uniform nodes, Jacobi Polynomial, Rate of Convergence, Lagrange Interpolation, Hermite-Fej er interpolation.