Lagrange interpolation | Programming Numerical Methods in MATLAB

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The theory and MATLAB programming steps of Lagrange's interpolation method are explained.
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[@equiknox_]

Hey, just wanna let you know that I am thankful I found this video. My prof does not even taught us how to code and he expects us on exam that we code things like this on octave. You are really helpful even years have already passed. Thank you!!

[@teerachote]

I just getting into all of this Matlab thing and this video explain it crystal clear, Thank you so much!

[@tayneilson]

wish i found this sooner. i bought your materials keep up the good work

[@AJ-et3vf]

Awesome video! Thank you! You're very helpful and your voice is very calming and soothing. Thank you!

[@bastianrojo6175]

Thank you very much, Mr. It helped me a lot. Greetings from Chile

[@vma011]

Thank you so much! You helped me solve a problem of my numerical methods class. Instead of evaluating a single "xp" value, we needed to plot the resulting polynomial as a function, so I had to vectorize the calculation. I generated a vector xp = linspace( min(x), max(x), 200) and initialized the sum and product variables as vectors with dimension 1x200 . I then used exactly your same algorithm but used point-wise product (.*) and division (./) where needed. I solved the thing in few lines thanks to your code!

[@AJ-et3vf]

Awesome!

[@Sojung0714]

that's so simple! Thanks a lot!

[@shaimashakib6409]

Thank u so much ! This helped me A LOT :D

[@alobyerl7635]

Hi! Thank you for the video, I have one more question, how to generate the plot for that equation?

[@bcerme16]

Thank you very much sir! It helped me a lot

[@ismailamdah2937]

Thank you very very much!

[@sagarraj4521]

Thanks a lot sir!!!!

[@ritucreativity3889]

Thank you so much ❤

[@sethmcbrown9492]

You're awesome bro

[@joelelanga4882]

Thank you very much

[@sylwiawrzesien518]

Hello thank you for your tutorial. Could you tell me how to plot it ?

[@user-ok8wy2vx7b]

thank you!

[@carlospuente3979]

Hey! I have a question: why does pr start at 1? I mean, I know why, but in the code I don't understand why is it there.

[@mpixlas4]

Great video, thank you very much. I'm trying to figure out how to plot the respective fit... Any thoughts about that?

[@mechtutorcom]

Thank you for the comment. The curve can be plotted by adding x array from x0 to xn. The Lagrange interpolation routine should be put inside a for-loop which calculates y-array element corresponding to each x-array element. At the end, two arrays of x and y can be plotted easily with MATLAB plot function. You can find this technique applied at the end of this video of Lagrange interpolation with Python: kzbin.info/www/bejne/moWqooKgZrONrbs

[@AJ-et3vf]

For loops

[@DeGameBox_SRBT]

thanks! thanks! thanks! you just saved my studwork! @@mechtutorcom

[@oussamaguerroudj9053]

thank u ^^

[@agustinacevedo5932]

Excellent work but I have a doubt, if I wanted to know the coefficients of the lagrange polynomial, what should I modify the code that you developed? Thank you

[@sophia2928]

i have the same doubt

[@AJ-et3vf]

You will need a symbolic Computer Algebra System (CAS) in order to do that since the code only works for numerical evaluations and not symbolic manipulation of variables. If you really want the coefficients of the polynomial, use Vandermonde matrix polynomial to solve the problem. However, be aware that the resulting matrix may be ill-conditioned.

[@AJ-et3vf]

You don't have a doubt. You have a question

[@AJ-et3vf]

@@sophia2928 you don't have a doubt. You have a question.

[@AJ-et3vf]

@@sophia2928 You will need a symbolic Computer Algebra System (CAS) in order to do that since the code only works for numerical evaluations and not symbolic manipulation of variables. If you really want the coefficients of the polynomial, use Vandermonde matrix polynomial to solve the problem. However, be aware that the resulting matrix may be ill-conditioned.

[@mamtakapoor2600]

Very good

[@smailkhal]

Hello, i hope you reply to me. Can we write this program without using *if*? and how to replace *n=length(x)* with *size*

[@mechtutorcom]

Hello. Thank you for the comment. Instead of if-statement, you may use a while-loop. But, you will still need a counter for j values. I believe using if-statement, as shown in the video, is much simpler. The size() function is more general than length() because it works with 2, 3 and higher dimensional arrays. In this program, both size() and length() work similarly. The difference is the array return value in size(). For example, [m] = size(x); n = m - 1; I hope I could answer your question.

[@gricelbarrera6472]

thanks!!

[@user-ik5xm8ci7i]

Please, if you are reading this, tell me - why is the " pr " (product variable) equal to one and not any other number?!

[@vesto6864]

Thanks

[@sukranochani5764]

thanks 👍👍👍👍

[@bingxinyan8103]

Great

[@mervedenizyldz4226]

Thank you so much for this great explanation. Can you help me with how to obtain the exact polynomial of degree n fitting the data points we have? What should I add to the code you have written in the video? Thanks.

[@mechtutorcom]

Thank you Merve for your comment. The degree of polynomial in Lagrange interpolation depends on the number of the given x,y points. If you need to change the degree, you have to increase or decrease the points.

[@mervedenizyldz4226]

@@mechtutorcom Thank you so much , I am going to try it.

[@MuhammadBilal-bu3wc]

I have repeated the same code as that of you but my answer doesn't matches. So could you please help me out?

[@mechtutorcom]

The code in the video was run on Octave. If you're using MATLAB, some small changes might be needed to have matching results. You can copy and paste your code here, and I will certainly check it.

[@stonedcodingtom9097]

thx

[@equiknox_]

Why is sm = 0??

[@alexanderotalvaro6819]

mister , por que no me arroja resultado , espero su respuesta pa ya , gracias por la atención prestada

[@mechtutorcom]

Without seeing your code, it is difficult to know why it does not give results. Is there an error message?

[@rabid6767]

jys n bees

[@anujitmaity0722]

Poor voice