CMPSC/Math 451. Feb 25, 2015. Gaussian Quadrature. Wen Shen

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9 жыл бұрын

Wen Shen, Penn State University.
Lectures are based on my book: "An Introduction to Numerical Computation", published by World Scientific, 2016. See promo video: • Book Promo: An Introdu...

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@nomimino3414 5 ай бұрын

Thank you for explaining where the symmetry and the constants for the weights come from (and also the linear transformation)!

@mahmoudraafat4885 7 жыл бұрын

excellent and very smooth explanation. I am a part time professor at university and was looking for an answer to the symmetry conditions to simplify the formulas and looked several places and you explained it (only one to explain it)...deeply appreciated Wen Shen

@wenshenpsu 7 жыл бұрын

Thank you for your kind comment.

@dihydroxyacetonep04 8 жыл бұрын

She's really good.

@wenshenpsu 8 жыл бұрын

+dihydroxyacetonep04 Thanks.

@dusannavratil102 7 жыл бұрын

Thank you very much from Czech Republic, it really helped me understand this topic! Great explanation :)

@wenshenpsu 7 жыл бұрын

Thanks!

@JohnWick-xd5zu 2 жыл бұрын

You're a gifted explainer! Thank you from Egypt

@wenshenpsu 2 жыл бұрын

You're so welcome!

@mingmiao364 4 жыл бұрын

Fantastic lecture!!

@lounesbenali4889 2 жыл бұрын

It took me a certain time to understand all what is going on here but now that I understand it is a all pleasure Thanks !

@tmp544 2 жыл бұрын

15:05 Can u explain how this proof works? for example 17:06 even though the method is true who says the coefficients A0 and A1 are not different for any chosen f(x) (f=1 or f=x or f=x^2)

@Archeopteryx 9 жыл бұрын

awesome teacher!

@wenshenpsu 8 жыл бұрын

+Archeopteryx Thanks!

@zwazwezwa 4 жыл бұрын

Great lecture!

@nimnim5149 2 жыл бұрын

Thank you for the great lecture ...

@nias2631 9 жыл бұрын

Awesome! Very clear explanation!

@wenshenpsu 8 жыл бұрын

+brian whitener Thanks.

@matarloum2894 8 жыл бұрын

Thank you from Italy :)

@wenshenpsu 8 жыл бұрын

You are very welcome.

@Blendershick 3 жыл бұрын

Amazing thank you

@charitymdaka8230 9 жыл бұрын

Thank you. This is very helpful.

@wenshenpsu 8 жыл бұрын

+Charity mdaka I am glad that it is helpful to you.

@adayinmongolia1538 6 жыл бұрын

thank you so much for the very good lecture

@wenshenpsu 6 жыл бұрын

Thanks for watching.

@burakbayram4773 8 жыл бұрын

It's been really usefull, thank you

@wenshenpsu 8 жыл бұрын

+Burak Bayram Thanks for your comment.

@zhaoc033 6 жыл бұрын

Thanks you so much Prof. Shen. This is literally the best math lecture I have ever had. I wish I could sit in the classroom and be one of the students. Plus, I appreciate that you are replying to pretty much every comment on youtube. One quick question for you. Do numerical optimization methods (such as quasi-Newton or L-BFGS-B algorithm as implemented in Scipy) also fall into the realm of numerical analysis as well?

@wenshenpsu 6 жыл бұрын

Those are numerical methods for optimization, which in itself is a large field. However, I do not have videos on this topic. I might consider making some videos in the future. Thanks for watching and for your kind comments.

@johnmaduka1209 7 жыл бұрын

Nice explanation!!!!, was helpful to me in this Chapter . I am student from Tanzania.Nice job Wen Shen.

@wenshenpsu 7 жыл бұрын

Thank you!

@ehza 7 жыл бұрын

Great one :)

@ivanwaako2525 4 жыл бұрын

thank you. from shanghai

@huailongshi553 8 жыл бұрын

it’s very good.

@wenshenpsu 8 жыл бұрын

+Huailong shi Thanks for watching.

@hafizmasum9600 6 жыл бұрын

Excellent

@wenshenpsu 6 жыл бұрын

Thanks.

@wenshenpsu 5 жыл бұрын

Thanks for watching!

@maheshnmurthi 9 жыл бұрын

Notation may be made clearer by subscripting f with the power of basis function.

@wenshenpsu 8 жыл бұрын

+Mahesh Narayanamurthi (mnm) Thanks for your comment. I agree. :)

@dhruv3585 3 жыл бұрын

Teacher can you tell advantages, disadvantages and applications of Gaussian quadrature

@iphykelvin8698 4 жыл бұрын

I have a question. Why can we use this for any interval of integration [a,b] and not for only [-1,1]. Thanks

@xtr3m385 2 жыл бұрын

Actually, you can use the method for any interval [a, b] you just have to map the original interval [a, b] to [-1, 1] first. Check 33:58

@trexbattle 2 жыл бұрын

Wow she uses a chalk board that’s how you know she knows her stuff. Jesse Barlow is a PowerPoint professor

@tmp544 2 жыл бұрын

15:05 Can u explain how this proof works? for example 17:06 even though the method is true who says the coefficients A0 and A1 are not different for any chosen f(x) (f=1 or f=x or f=x^2)

@alexmzadeh 8 жыл бұрын

I think the degree of precision of the n-node rule is 2n-1, not 2n+1.

@wenshenpsu 8 жыл бұрын

+Alex Z Yes, you are right. But I used (n+1) to denote the number of nodes, so we are both right.

@alexmzadeh 8 жыл бұрын

+wenshenpsu thank you for the clarification.

@user-to9yc8sv7l 4 жыл бұрын

Can this method be applied to solve the Friedholm integral equation?

@juleshetzler9665 5 ай бұрын

@untold9047 7 жыл бұрын

plz do 4 point

@foolhardby 5 жыл бұрын

疼痛熙跛鸭

@bjthinks 8 жыл бұрын

The audio is in stereo format, but the right channel is blank. Very annoying to listen to.

@wenshenpsu 7 жыл бұрын

Sorry for that. The technician did the recording.

@bjthinks 7 жыл бұрын

And, thank you for the great lecture. I used this, together with other sources such as Golub & Welsch 1969, to implement the rendering in my android app: play.google.com/store/apps/details?id=com.gputreats.orbitalexplorer . Weighted Gaussian quadrature rules are calculated in advance and used on the GPU for rendering. This was the best lecture I found on GQ.

@wenshenpsu 7 жыл бұрын

Thanks again.

@juleshetzler9665 5 ай бұрын

well you're annoying, Brian. i personally think it's soothing