Convergence and norm estimates of Hermite interpolation at zeros of Chevyshev polynomials

Abstract

In this paper, we investigate the simultaneous approximation of a function f(x) and its derivative by Hermite interpolation operator based on Chevyshev polynomials. We also establish general theorem on extreme points for Hermite interpolation operator. Some results are considered to be an improvement over those obtained in Al-Khaled and Khalil (Numer Funct Anal Optim 21(5–6): 579–588, 2000), while others agrees with Pottinger’s results (Pottinger in Z Agnew Math Mech 56: T310–T311, 1976).

Survey of Hermite Interpolating Polynomials for the Solution of Differential Equations

“…Al-Khaled and Alquran [24,31] investigated the simultaneous interpolation of function f (x) and its derivative f (x) by using the Chebyshev-polynomial-based Hermite interpolation operator H 2n+1 . In the case of Hermite interpolation, a theorem on extreme nodes was established by the authors that agreed with Pottinger's results [32] and was an improvement of the results obtained in [25].…”

A numerical algorithm for solving the Cauchy singular integral equation based on Hermite polynomials

“…The convergence and norm estimates of the Hermite interpolation at the zeros of the Chebyshev polynomials are investigated by Al-Khaled and Alquran [2].…”