Local Vs Global Interpolation Methods | Numerical Methods

Let’s talk about the differences between local vs global interpolation methods in numerical methods or any course where interpolation is taught. Let’s begin with global interpolation methods. The key difference between a global vs a local interpolation method is the amount of our data set that we are going to use to find the interpolating polynomial. A global interpolation method is going to use all data possible to it to find the interpolating polynomial, whereas, a local interpolation method is just going to use some subset of that total data. An example of a local interpolation method is spline interpolation, which will be talked about over the next couple of videos. So, if you can imagine this rectangle here with all our possible data points contained within it, this is the only data we can use when creating a global interpolating polynomial, meaning no matter what method we use, be that Lagrange interpolation or newton’s divided difference method, we are always going to get the exact same interpolating polynomial.

This timeline is meant to help you better understand Local Vs Global Interpolation Methods: 0:00 Introduction. 0:34 Interpolation Process 1:06 Local Vs Global Interpolation Method Differences 3:40 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/playlist?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 #interpolation ... https://www.youtube.com/watch?v=CzsioRMxdIU