Constrained mock-Chebyshev least squares approximation for Hermite interpolation

TL;DR

This paper introduces an extended constrained mock-Chebyshev least squares method for Hermite interpolation, effectively reducing Runge phenomenon and improving approximation accuracy using both function and derivative data.

Contribution

It presents a novel extension of the mock-Chebyshev least squares technique specifically for Hermite interpolation, incorporating derivative information.

Findings

Enhanced approximation accuracy demonstrated through numerical experiments

Effective mitigation of Runge phenomenon in Hermite interpolation

Method outperforms standard polynomial interpolation approaches

Abstract

This paper addresses the challenge of function approximation using Hermite interpolation on equally spaced nodes. In this setting, standard polynomial interpolation suffers from the Runge phenomenon. To mitigate this issue, we propose an extension of the constrained mock-Chebyshev least squares approximation technique to Hermite interpolation. This approach leverages both function and derivative evaluations, resulting in more accurate approximations. Numerical experiments are implemented in order to illustrate the effectiveness of the proposed method.