Determining the Rolle function in Lagrange interpolatory approximation

TL;DR

This paper introduces a method to identify the Rolle function in Lagrange interpolation via differential equations and proposes an enhancement device that leverages this knowledge to improve approximation accuracy.

Contribution

It presents a novel approach to determine the Rolle function in Lagrange interpolation and introduces a device to enhance approximation quality.

Findings

Successfully determines the Rolle function using differential equations.

Proposes a device that improves Lagrange approximation based on Rolle function knowledge.

Provides a new tool for more accurate polynomial interpolation.

Abstract

We determine the Rolle function in Lagrange polynomial approximation using a suitable differential equation. We then propose a device for improving the Lagrange approximation by exploiting our knowledge of the Rolle function.