Lagrange Interpolation Method: Algorithm, Computation and Plot | Numerical Computing with Python

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Lagrange interpolation (or Lagrangian interpolation) method is one of the most basic and common methods to apply the interpolation polynomials. It was named after the great mathematician Joseph-Louis Lagrange (1736-1813). This tutorial explains the Lagrangian polynomial form of the interpolation function, the algorithm of the method and the Python code by using Python lists with basic for loops and by using the Numpy arrays by using conditional slicing in addition to plotting the interpolation function versus the given data points by using matplotlib.pyplot module.
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[@asifahmed1801]

cool ! This is one of the best explainaton i have ever seen regarding numerical python subjects

[@JD002]

The best explanation ,it was so lucid that I don't need to learn from anywhere about this topic any further, thanks a lot. ♥

[@AJ-et3vf]

Great video sir! Thank you! You explain very well and your voice and video are very soothing and calming. Very nice to listen to.

[@ignatiolu863]

Just what I was looking for, sir! Great video!

[@IndrainKorea]

Thank you for the tutorial! I like the way you explain it too, very clear!

[@DeGameBox_SRBT]

thanks! thanks! thanks! you just saved my studwork!

[@wolnyczowiek8705]

Thank you so much that was exactly what i was looking for

[@victorcunha8874]

Espetacular, grande abraço do Brasil

[@MathPhysicsFunwithGus]

Amazing video can't wait for more!

[@angelortiz3564]

Cool video. Really help me understand this algorithm. I have one questions tho. Given that the code is reseting the yp value every time it calculates, and in truth, the yp values depends on the previously calculated, isn't there a way to use the sum of the previously calculated yplt terms?

[@CAMiiKatze]

great. Blew my mind how you can do it in so little lines ! :)

[@manashdey8765]

Very nice explanation sir 😊.. thank you ,

[@anshu_raj_]

Thank you so much

[@2hp_logam498]

why is there n + 1 ?

[@flamazx1]

Earned a suscriber, thanks!!!!

[@kudakwashechirinda5652]

Thanks this is really helpful

[@sandeepgodiyal5686]

Thanks for this wonderful course. Can you please help for a small problem for polynomial fitting (4-5 order) of data and to find out regression coefficients?

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[@amvro23]

A similar more comprehensive perpective import numpy as np x = np.linspace(0,100, 6) y = np.array([26.0, 48.6, 61.6, 71.2, 74.8, 75.2]) def lagrange_interpolation(x, y, xp): n = len(x) - 1 # degree of the polynomial index_i = range(n + 1) index_j = range(n + 1) p_values = np.array([np.prod([(xp - x[j]) / (x[i] - x[j]) for j in index_j if j != i]) for i in index_i]) yp = p_values.dot(y[index_i]) return yp lagrange_interpolation(x, y, 50)

[@user-gs6nx7jh5j]

Very useful! Thanks a lot!

[@syahputra8777]

thanks you sir great video and clear explanation.. btw I really hope you can explane a litle bite description of how to plot lines in linear regression or polinomial regresion. Thanks you

[@hadimajdi9272]

spectacular , thank you so much

[@Matchless_gift]

Great work sir#mathsbeetle

[@karimlimos8541]

thank you sir for this video

[@agustinhernandez4261]

Hi, your video is helping me to do a university homework but the teacher want to know what was the polynomial, So i dont have to input the X value. How can i do in order to get the polynomial?

[@agustinhernandez4261]

cuz then i have to integrate it

[@LoganKaleva]

I know this video is old, but i'm copying the code line for line and it's saying my i isn't defined for yp +=

[@erfanjavaheri398]

Sir i want for n points how can i do that?

[@farhanrafid8584]

thank you so much.

[@purib3992]

can you write code for differentiation to Lagrange's formula

[@sugandhasingh3833]

how to implement same method for any image?

[@isaacfernandez2243]

how can I calculate the error?

[@HuongHoang-ez9si]

ppval..Is this the method?

[@alexandrerocha9148]

There somethings wrong in your code, for example, if you take the xp = 90, the answer wasn't anyhing between 74.8 and 75.2

[@nicsim7469]

why was xp equal to 50?

[@KeremTatlc]

it is a value that you want to predict its y.You are giving the dataset, after than that you are giving an x value and algorithm is calculating it's y value

[@ayushigarewal]

why xp=50 pls explain

[@mechtutorcom]

Thank you for the question. xp represents the value of X which does not exit in the given data set, and we want to know the corresponding Y value of it. In this video, I used xp = 50 as an example only. You can choose any other value between 0 and 100.