An introduction to numerical integration through Gaussian quadrature

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This video explains how the mechanism behind Gaussian quadrature works, and how Legendre polynomials can be used to find the weights and x coordinates in the quadrature formula.
This video is part of a lecture course which closely follows the material covered in the book, "A Student's Guide to Bayesian Statistics", published by Sage, which is available to order on Amazon here: www.amazon.co....
For more information on all things Bayesian, have a look at: ben-lambert.co.... The playlist for the lecture course is here: • A Student's Guide to B...

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12 окт 2024

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Комментарии : 30

@draxonful 3 года назад

Thanks for the detailed explanation! Really helps for our numerical methods module at uni! Best regards from Germany!

@CodeVault 6 лет назад

24:05 You forgot to cut there ;) Otherwise, the only helpful video I found about this topic, really made me understand what's up with Gaussian Quadratures. Thanks!

@SpartacanUsuals 6 лет назад

Thanks for pointing this out. Best, Ben

@sumitmukherjee249 3 года назад

That graphical depiction was really interesting.

@quanttube 2 года назад

This absolutely magnificently beautiful Mr. Lambert. Thank you so much for posting this.

@el-shammahrushwaya9677 5 лет назад

why didnt you work out the ws and xs, wasnt that the whole point of using this formula?

@chimetimepaprika 3 года назад

Did you discover the Lambert W function? Tee hee hee. Great video, mate! Neat and tidy explanations!

@MatheusSilva-dragon 3 года назад

You explanation is better than my teacher's pdf file!

@thomasfranzstockhammer7846 2 года назад

Thank you so much ! Best regards

@AuroraClair 5 лет назад

Waw, thanks for the detailed explanation. I was just wondering, maybe a silly question but still, how come we are only using odd-order polynomials for determining weights and locations for evaluating functions? Is there an explanation for this? Thanks again Is it because the number of unknowns is always even?

@PaulJ_81 3 года назад

exactly

@tusharbommala8150 3 года назад

thank you for the detailed explanation. I really appreciate it

@starkillre 4 года назад

So one point I'm wanting to get perfectly straight, if you could help me understand. Doesn't this mean that, for intergration of finite intergrals of valid f(x), the weighs and values of x are effectivly always known? and that the actual issue is figuring out which point you specifically want?

@AJ-et3vf 2 года назад

Awesome video! Thank you!

@Fundamental_Islam. 5 лет назад

How did u find w1 2 x1 etc

@protyush18 3 года назад

What kind of quadrature can be used for double integrals and functions with singularities?

@kavehsiah4021 Год назад

So, what happens if your polynomial is of an even order or a non-integer order?

@김승환-g3c 4 года назад

Thank you!! I can understand it!!!

@JacekKarwowski 4 года назад

After calculating the Lagrange polynomial, why not just use its integral as the approximation of the integral of f? I get that the answer is probably "because Gaussian quadrature is better", but why is it better? In the simulaton showed in the video, it seemed that the integral of polynomial had a much smaller error than the value you got from sampling.

@mariovelez578 Год назад

It's the same thing. As he said in the video, gaussian quadrature for polynomials is an exact approximation, but is a lot faster since it uses less calculations.

@cfcalle 4 года назад

Amazing explanation. Thank you very much!

@finite_elements 3 года назад

Thank you

@ismaelerroussi9704 3 года назад

masterclass 👏

@1827641 4 года назад

4:38 you meant \hat{f} instead of f, didn't you?

@tag_of_frank 5 лет назад

Where can I find this legendre table

@chickenkorma3163 4 года назад

Just google it. It is on wikipedia.

@ajeetgary9707 6 лет назад

For your example you did something that happens to work out exactly - it's a linear approximation, manufacturing a serendipitous example is misleading to how good the first step of the algorithm actually is.