Introduction To Spline Interpolation | Numerical Methods

Let’s talk about what spline interpolation is in this Introduction To Spline Interpolation video. If you recall, in our past interpolation methods videos we constructed a polynomial from all discrete data points that were supplied to us and made a global polynomial interpolating function. By global we mean that we used our whole data set and not some section of it to develop the interpolating polynomial. Therefore, as I have previously mentioned, it doesn’t matter if we used Lagrange interpolation or divided difference interpolation, both methods will result in the same global interpolating polynomial as they take in and output the same result. Although great in some scenarios, sometimes using a global interpolating method is impractical or less efficient than simply taking a local interpolation. Why though? Well as we add more data points to a global interpolating polynomial, we need to increase the polynomial order, which in certain applications can give widely inaccurate answers

This timeline is meant to help you better understand spline interpolation is in this Introduction To Spline Interpolation video:
0:00 Introduction.
0:12 Brief recap of interpolation purpose
0:32 Recap of Global Interpolation interpolation algorithms
1:11 Problems with global interpolation algorithms
1:57 Global vs local interpolation algorithms
2:23 Types of spline interpolation
3:40 Outro

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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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[helenkarimakwenda]

Hey StudySession! Thanks for the useful explanations, they are all great!... Just would like to find out when might the spline interpolation example video be coming out?

[shalabi]

First of all thanks a lot, your theaching is much much better than my nomarical methods professor, so now I think I have a better chance of passing the couse. When is the next video? I really need to learn more about cubic spline 😁😅

[thatguyoverthere]

Why is cubic spline not considered 3rd order?

[EW-mbih]

at 3:10, cubic spline is 3rd ordrer polynomial, not 2nd ordrer which would be quadratic spline

[courtneyshafer]

Thank you so much for your videos, they've been helping a lot with my numerical analysis course. Will you be uploading any videos on trigonometric interpolation?

[SJr]

Hy, around 3:20 isnt that quadratic spline instead of cubic? Thank you for the wonderful explanations too ! 🙏

[Yazan_Majdalawi]

Shouldn't the second-order polynomial be called quadratic?