Newton Divided Difference Interpolation (Intuition and Formula) | Numerical Methods

Let's talk about Newton Divided Difference Interpolation and the intuition and formula it uses.
In Newton's 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. In this video we will go through a Newton divided difference interpolation derivation and the newton divided difference interpolation intuition.
Links that will help you learn:
Introduction to Interpolation: • What is Interpolation?...
What are polynomials: • What Are Polynomials?
2nd Order Newton Polynomial Derivation: • Interpolation - Newton...
This timeline is meant to help you better understand Newton Divided Difference Interpolation:
0:00 Introduction
0:07 What is Newton 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: • Numerical vs Analytica...
Numerical Methods Examples Playlist: • Jacobi Iteration Metho...
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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..
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[@anonymous-3720]

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[@Smith-wl]

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[@pauselab5569]

nice connection with the polynomial being like a taylor series. the divided differences feel a lot like derivatives mesuring the rate of change of a discrete function.

[@abdulhamedeid935]

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