CMPSC/Math 451. March 20, 2015. Gauss-Seidel, SOR. 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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@johnch2800 3 жыл бұрын

I can't begin to explain how much I admire your way of teaching. Truly thankful.

@deborahfranza2925 4 жыл бұрын

I loved how you lead first with simple examples, and then generalized the fixed point iteration forms for Jacobi and GS. It really helped me understand what was going on! Thank you so much!

@rajshikhargupta6024 7 жыл бұрын

Thank you for making it so clear, the SOR.

@wenshenpsu 6 жыл бұрын

Thanks for watching.

@AJ-et3vf 2 жыл бұрын

This is very invaluable lecture maam. I especially highly appreciate your expressing the jacobi and also the gauss-seidel iterations into matrix form which to me is so much more understandable and less intimidating than the usual summation notation form. Thank you so much

@nauyupoahz6662 7 жыл бұрын

Wish you were my prof

@wenshenpsu 7 жыл бұрын

Thanks for watching.

@month11th 7 жыл бұрын

Not until I found this video that I totally understand SOR, thank you!!

@wenshenpsu 6 жыл бұрын

Thanks for your comment.

@01MeuCanal 7 жыл бұрын

Many many thanks for you class Prof. Wen!

@wenshenpsu 6 жыл бұрын

Thanks!

@Mrr1503 5 жыл бұрын

Well explained, thank you!!

@milliekim5072 4 жыл бұрын

Awesome, thank you professor!!!!

@AJ-et3vf 2 жыл бұрын

Thank you so much for your lectures Maam. Very clear and helpful!

@worawatnakawiro466 5 жыл бұрын

Very well explained, Prof.

@farhanomar7839 6 жыл бұрын

You are very good in explaining and you were brilliant in explaining each step you were doing . Thanks

@wenshenpsu 6 жыл бұрын

Thanks!

@MegaArti2000 4 жыл бұрын

That was a lot helpful!!! Thx from Brazil :)

@AnupKumar-wk8ed 7 жыл бұрын

Fantastic lecture! Thanks a lot mam!

@wenshenpsu 7 жыл бұрын

Thanks.

@TheMarcindec 7 жыл бұрын

Thank you very much for a concise explanation!

@wenshenpsu 7 жыл бұрын

Thanks for watching.

@ahmad97ist 7 жыл бұрын

Thank you! Was extremely helpful and clear.

@wenshenpsu 7 жыл бұрын

Thanks!

@amineo.7553 8 жыл бұрын

Thank you very much and kind regards from Germany !

@wenshenpsu 8 жыл бұрын

+Amine O. Thanks for watching. Danke.

@indrapambudi6877 6 жыл бұрын

Hello prof, nice explanation. I want to ask something. Since in the SOR equation it's bi - sigma() - sigma(), at 30:35 you wrote 0.6(1+x1 [k+1]+x3[k]) instead of 0.6(1-x1[k+1]-x3[k]). Can you please explain?

@dr.mohammadziazahedi2844 7 жыл бұрын

Everything is very nice and helpful. Thanks a lot. May I ask that Gauss-Seidel is true or Gauss-Seidal?

@wenshenpsu 7 жыл бұрын

Thanks! Gauss-Seidel. My typo.

@trackmyactivity 5 жыл бұрын

You are so good!

@wenshenpsu 5 жыл бұрын

Thanks.

@sca2777 7 жыл бұрын

great lesson ! very clear and easy

@wenshenpsu 6 жыл бұрын

Thanks for watching.

@birhanubetela7373 5 жыл бұрын

very clear lecture!!!!! Thank you so much!!

@wenshenpsu 5 жыл бұрын

Thanks!

@dawooddawood1633 5 жыл бұрын

brilliant teacher,

@wenshenpsu 5 жыл бұрын

Thanks!

@fathifathi5064 6 жыл бұрын

Hi, I want to help solve the question NUMERICAL METHODS FOR DIFFERENTIAL EQUATIONS

@CarlosDominguez-yr1ic 7 жыл бұрын

Professor Wen Shen: Penn State University, USA. Hi Professor Wen Shen. I would like to inform you that I detected a small mistake at the minute 31:46 of this video. You wrote in the blackboard for the first iteration with over relaxation: X(1) = ( 0.3, 1.28, 1.708 )T and the correct numbers should be X(1) = ( 0.3, 1.28, 1.768 )T I mean that 1.708 should be corrected and replaced by 1.768 VERIFICATION: X(0)=(0,0.5,1)T X1(1)=-0.2X1(0)+0.6X2(0)=-0.2(0)+0.6(0.5)=0.3 X2(1)=-0.2X2(0) + 0.6(1+X1(1)+X3(0))=-0.2(0.5)+0.6(1+0.3+1)=-0.1+0.6(2.3)=1.28 X3(1)=-0.2X3(0)+0.6(2+X2(1))=-0.2(1)+0.6(2+1.28)=-0.2+0.6(3.28)=1.768 The video shows 1.708 instead of 1.768 The second iteration was correct. I hope that this information was useful for you. I programmed a macro of Excel to calculate 5 iterations of Gauss Seidel with over relaxation using ω=1.2 and I got the following results: n x1(i) x2(i) X3(i) 0 0 0.5 1 1 0.3 1.28 1.768 2 0.708 1.8296 1.94416 3 0.95616 1.974272 1.9957312 4 0.9933312 1.99858304 2.000003584 5 1.000483584 2.000575693 2.000344699 My name is Carlos Vicente Dominguez. I am a graduate student of the specialization in electric power systems at Central University of Venezuela in Caracas. Best regards from Venezuela.

@wenshenpsu 7 жыл бұрын

Thanks so much for finding this "very-hard-to-find" typo. I will put an annotation in the video!

@HassanHassan-np8rf 6 жыл бұрын

Thank you so mush.

@wenshenpsu 6 жыл бұрын

Thanks.

@mehwishkhalid1016 6 жыл бұрын

How can find absolute errors for each iteration

@akhileshsingh7269 7 жыл бұрын

Is there any criteria for finding best possible value of w(omega) for faster convergence.?

@wenshenpsu 7 жыл бұрын

This requires more analysis. You should find the w that minimizes the norm of the iteration matrix, which is a nontrivial task.

@anik8559 3 жыл бұрын

22:00 SOR Method

@sangeetarawat9470 6 жыл бұрын

you made it very easy for every one, thank you mam

@wenshenpsu 6 жыл бұрын

Thanks for watching!

@abdulnaveed4984 8 жыл бұрын

how to find omega in sucssive over relexation method please also explain it

@wenshenpsu 7 жыл бұрын

you should choose it to be between 1 and 2. Try 1.5. For many problems, the best omega is usually between 1.5 and 1.9. Thanks for watching.

@leigap 6 жыл бұрын

Is there any video about SSOR method? thanks.

@wenshenpsu 5 жыл бұрын

I don't have a video on SSOR. :(

@farhanomar7839 6 жыл бұрын

I noticed sothing her ,if we are calculating x2 at index k+1 why not using it in calculating x3 at index k+1 insted of using the one at index k? it is not better for convergenc?

@wenshenpsu 6 жыл бұрын

Yes you can do that. We took the Jacobi as an example, to form SOR. You can certainly use GS. Thanks!

@alanaalana463 7 жыл бұрын

hi plz help me i have one day before exam

@alhammadi1987 8 жыл бұрын

very good thankssssssssss

@wenshenpsu 8 жыл бұрын

+gaber alhammadi Thanks!

@abdulnaveed4984 8 жыл бұрын

please help

@johngeller2113 8 жыл бұрын

The book is a little expensive for a graduate student. BTW, I noticed you said Gauss-Seidal. I think it should be Gauss-Seidel.

@wenshenpsu 5 жыл бұрын

I have promo code for my youtube viewers. See description on my promo video for the code. With that the book costs very little.

@bssyedphdmathematics8309 7 жыл бұрын

how got w or why should some think about w there must be some mathematical reason

@itsnotallrainbowsandunicor1505 7 жыл бұрын

In the following paper, engineering.jhu.edu/fsag/wp-content/uploads/sites/23/2013/10/JCP_revised_WebPost.pdf there is mention of Richardson's paper (see [5]), where you will find the origin of w as the ratio of amplitude of vibration on page 320. You can find Rischardson's paper listed at rsta.royalsocietypublishing.org/ It's not an easy read, but what you will find in solvers mentioned in many papers is this notion of oscillation as one tries to arrive at a solution. It is unfortunate that much of the theories are truncated for undergraduate students that they miss what is really going on behind the mathematics.

@wenshenpsu 7 жыл бұрын

The parameter w gives you flexibility. Detailed analysis on this is not suitable for this undergraduate course. Thanks for watching.

@haifa6004 4 жыл бұрын

Wen Shen Hong ;)

@sylvainZa 7 жыл бұрын

very good very good thanks keep it up

@wenshenpsu 6 жыл бұрын

Thanks!

@huameng 9 жыл бұрын

Clear Interpretation ! Very Helpful.

@wenshenpsu 8 жыл бұрын

+Hua Meng Thanks!

@vietdinh-van8018 4 жыл бұрын

I like you than mathematics.

@joezhang839 6 жыл бұрын

You got the name wrong :( It's Gauss-Seidel not Seidal...

@wenshenpsu 6 жыл бұрын

Thanks .

@michaelmuiruri3623 3 жыл бұрын

ARE THERE ANY REAL CALCULATIONS THAT YOU'VE DONE? ESPECIALLY FOR A NON DOMINANT DIAGONAL MATRIX.

@felipemaster532 3 жыл бұрын

If it is a non dominant diagonal matrix its most likely not to converge to a solution

@fffppp8762 5 жыл бұрын

I coded SOR and compared the number of iterations. But SOR's number of iterations turns out to higher than Gauss-Seidal's , which is counter-intuitive