Linear Algebra 12c: Applications Series - Polynomial Interpolation According to Lagrange

[kpmaynard]

Thank you so much for this absolute gem of an explanation of Lagrange polynomial interpolation Professor Grinfeld.

[muhammedcansz]

Awesome! This video also proves how math is beatiful not just lagrange interpolation

[Wawadish]

What a great video, I knew how to use the formula but never understood the concept. You made me enjoy math a lot more, I wish all my teachers would explain exactly how the concepts work just like you did. You are amazing!

[BudskiiHD]

Best math content on youtube, primarily because the concepts are explained so well. Thank you very much!

[davidmuhr]

Wow, that was by far the best explanation of Lagrange polynomials, thank you!

[tiddlywinks]

Such a simple concept but I just couldnt understand the derivation before this!

[aldomaresca]

Very clear and helpful, thanks for making internet a better thing

[subhadeepbej]

This was so wholesome. We must protect him at all cost.

[DigheVijay]

Really good explanation of the concept. Thanks a lot

[PuleMC]

Wow👏thanks a million🤭that's perfectly clear

[geographymathmaster]

I found your content very helpful.
Thank you very much and God bless. :)

[coenrijna]

Thank you so much, amazing explanation!

[juustgowithit]

THANK YOU SO MUCH I FINALLY UNDERSTAND

[vineetmukim]

In the previous approach, we could fit a higher degree polynomial too with extra DOF. How to do it using Lagrange Polynomial Interpolation? Choosing input points randomly and putting constraints to have STRAIGHTish behavior e.g. P5(5)=1.1, P6(6)=1.3 etc?

[georgeorourke]

By the way which program do you use to plot your grapha / sovle you matricies? I looks like a Mac screen. Thank you

[agh]

Who are your top 5 mathematicians of all time?

[thearkpearl]

I think that the most difficult part to digest is to have Polynomials that are linear independent but JUST for some particular values of x! Which makes me think... Can two quadratic polynomials be linear independent for any value of x ??? or is this just another "fancy math trick" ?

[hericklenin]

Hello Professor, nice lectures, thank you so much for them. Question: does the "shape" of the cloud of points has to do with the choice of basis decision? Is there some intrinsic information on the relative position of the points that would help in the decision?

[knivesoutcatchdamouse]

So am I to understand that he 4 cubic polynomials p_1, ..., p_4 that were constructed in this example are linearly independent? Otherwise they could not form a basis for the space of cubic polynomials. I suppose their linear independence follows from constructing each of them in such a way that p_n(x=n) = 1 and p_n(x) = 0 at x=/=n for n=1, 2, 3, 4? Something about having to take a multiple p_n in order to make sure the curve goes through a given y-value y_n=a at x=n, I.e., demanding the term 'a*p_n' to be included as part of the sum that you would get by decomposing the curve p(x) into a linear combination of the 4 p_i functions...

This seems likely to imply linear independence but I'm having a hard time explaining to myself the exact details of how the linear independence follows. Maybe by tomorrow evening I'll have the answer, but it's out of reach for my tired mind tonight. Very interesting video!

[omartaha]

How prove Pn(x) of newton equal Pn(x) of Lagrange