Lagrange Interpolation

A basic introduction to Lagrange Interpolation.

Chapters
0:00 Introduction
01:07 Lagrange Polynomials
03:58 The Lagrange Interpolation formula
05:10 The Resulting Polynomials

The product links below are Amazon affiliate links. If you buy certain products on Amazon soon after clicking them, I may receive a commission. The price is the same for you, but it does help to support the channel :-)

The Approximation Theory series is based on the book "Approximation Theory and Methods" by M.J.D. Powell:

This video was made using:
Animation - Apple Keynote
Editing - DaVinci Resolve

Supporting the Channel.
If you would like to support me in making free mathematics tutorials then you can make a small donation over at
Thank you so much, I hope you find the content useful.

[tombackhouse]

Dude you make stuff so clear, watching your videos feel like cheating.

[einstien]

I remember developing the interpolation polynomial formula in college for fun. My discrete math professor gave a puzzle to the class to come up with polynomials that for many integer inputs return prime number outputs. I switched the problem a little bit for myself in that I asked "how can I make a polynomial that passes through each of these arbitrary points?" And as I solved this puzzle on my own over the next two weeks I developed this interpolation method on my own and it felt so empowering.

I showed it to a few of my other professors and we proved that there is only one line passing through two points, only one parabola passing through three points, only one cubic passing through four points, only one quartic passing though five points, etcetera for all natural numbers of points.

Anyway, some of my most enjoyable days of college were solving these puzzles.

[Peter-bgku]

Great video! Now it all makes sense. When I studied Lagrange polynomials, I only understood enough to work out the interpolation polynomials but never really grasped the intricate details behind them. Your video - like your other video of Pade approximations - has made the whole concept a lot clearer to me. Thank you!

[whitewalker]

I swear this Lagrange guy is everywhere. Every field of math I'm trying to understand, something Lagrange pops up.

[allyourcode]

This can be used to create error correcting codes. The design of such a code is left as an exercise to the reader :P

[ricksoslick]

1 minute in and the visualization already helped more than hours of uni lectures

[purungo]

I love the way you explain things, its so straight forward and intuitive that it makes it feel like it's something I could've come up with. Really good explanations in this video and the Padé approximations, which I had never heard before. Thanks for making great content

[kojonketia]

Great explaination!. And I got this at the right time for my computational math class.

[asiimwemmanuel]

I've been using this video as a reference for quite a while and just realized it was released on my birthday. Thanks for all the guidance Dr. Wood ❤

[justdoityourself]

I love it when the video drops all the necessary knowledge in the first 30 seconds. Well done.

[AJ-etvf]

Wow! Awesome explanation! I particularly love how you broke down Lagrange polynomials into the smaller order polynomials that compose it and how those were "guessed" in the first place. Very intuitive explanation. Thank you!

[marcozelioli]

This was perfect. Why can't professors explain like this? Easy to understand with nice graphics for the visual learners + soothing voice that helps you concentrate. Thank you!

[jaminkidd]

I can tell this channel will be great for topics related to computational physics. Please keep it up!

[clementp.]

I'm a French student and I have to do researches on Lagrange interpolation theorem. Your video is the only that helped me understand the subject, not a single French video helped me on this.

[Angel-oqbs]

well, i'm actually dealing with maths in french, and it is my second language, but I swear that no french speaking professor on youtube was able to transmit this idea as smoothly as you did, sir. I appreciate that tysm...

[muess]

This is excellent. I've reviewed my materials and looked at a bunch of others online but this is far and away the best explanation I've found. Thank you!

[redroth]

Just found your channel and I really enjoy your videos!

[kangalio]

This is so beautiful

One aha moment after the other, effortlessly

[kiat]

Best explanation I've ever seen concerning Lagrange polynomials. I can now visualize proofs that use Lagrange interpolation.tysm

[max_kl]

Awesome video, got this in my recommendations just as the professor covered in my metrology class