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!
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?
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?
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.
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.
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.
Thanks for the detailed explanation! Really helps for our numerical methods module at uni! Best regards from Germany!
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!
Thanks for pointing this out. Best, Ben
why didnt you work out the ws and xs, wasnt that the whole point of using this formula?
That graphical depiction was really interesting.
This absolutely magnificently beautiful Mr. Lambert. Thank you so much for posting this.
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?
exactly
You explanation is better than my teacher's pdf file!
So, what happens if your polynomial is of an even order or a non-integer order?
thank you for the detailed explanation. I really appreciate it
What kind of quadrature can be used for double integrals and functions with singularities?
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?
How did u find w1 2 x1 etc
Did you discover the Lambert W function? Tee hee hee. Great video, mate! Neat and tidy explanations!
Thank you so much ! Best regards
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.
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.
Awesome video! Thank you!
Thank you!!
I can understand it!!!
4:38 you meant \hat{f} instead of f, didn't you?
Where can I find this legendre table
Just google it. It is on wikipedia.
masterclass 👏
Amazing explanation. Thank you very much!
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.
Thank you
would be nice if your lectures would include more intuition and less math to understand the concept
good explanation
This was terrible explanation, I got lost in first 8 min. :/