Divided Difference Interpolation & Newton Polynomials | Numerical Methods

In the divided difference interpolation method we use newton polynomials as our interpolating functions. A Newton’s polynomial are polynomials used to interpolate discrete data points from given data sets. but, you may ask, we have learned about Lagrange polynomials, why cant we just always use them? Well, newtons polynomials through divided difference has many advantages as it is faster, recursive and through such better, faster and much more widely used that Lagrange. We will talk about why this is the case later in the video.

Links that will help you learn: Introduction to Interpolation: https://www.youtube.com/watch?v=gT90n_J1hj8 What are polynomials: https://www.youtube.com/watch?v=Q2ajW5TUG0Y 2nd Order Newton Polynomial Derivation: https://www.youtube.com/watch?v=JJR3xALzKkw&t=1041s

This timeline is meant to help you better understand Divided Difference Interpolation: 0:00 Introduction 0:07 What is divided difference interpolation? 0:42 What are Newton Polynomials? 1:41 Newton polynomial formula 2:26 1st order divided difference derivation 3:49 Divided difference tables 6:18 Outro

Relevant Numerical Methods Playlists: Numerical Methods Playlist: https://www.youtube.com/watch?v=F2NWYEOHIkc&list=PLDea8VeK4MUTOBXLpvx_WKtVrMkojEh52 Numerical Methods Examples Playlist: https://www.youtube.com/watch?v=UA7bzwCwHMI&list=PLDea8VeK4MUTxZGOTG-VNnW4T3TYwlEc9

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This video is part of our Numerical Methods course. Numerical methods is about solving math problems through approximating the solution of problems that would be difficult or impossible to solve analytically. In this playlist we will cover topics such as solving systems of linear equations, solving systems of non-linear equations, numerical integration, numerical derivatives, etc.. #studysession #numericalmethods #newtonpolynomials ... https://www.youtube.com/watch?v=BAwOGkchq7w