Review New Application using Interpolation and Polynomial Approximation

This study analyses the mathematical structure of the interpolation to guarantee that the resulting function passes through all given data points. At the same time, polynomial approximation aims to find a polynomial function that closely matches the data but may not pass through all points and is typically determined using the least squares. Both methods have their advantages and are used in various fields, depending on the specific requirements of the problem at hand. The paper also explores the Lagrange Interpolation Error Theorem, providing insights into the accuracy and limitations of interpolation techniques. Understanding these methods and their error ata cteristiccs helps in selecting the appropriate approach for various practical applications.