CMPSC/Math 451: March 2, 2015. Fixed point iterations. 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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@essafr3823 Жыл бұрын

This is such a blessing, you were put on this earth to teach math. I've questioned my faith before, this lecture made me religious. Some people just end up where they're meant to be, you're one of them.

@edwincuevas9965 3 жыл бұрын

This is the BEST explanation of fixed point iterations I've seen. Thank you for sharing this!

@binni8507 5 жыл бұрын

As a penn state sophomore, I was really struggled about this math course util I watched ur youtube channel. Thanks a lot.

@loloioi 7 жыл бұрын

Thank you for explaining it so well! The fixed point iteration makes so much more sense to me now!

@wenshenpsu 7 жыл бұрын

Thanks!

@Mare_brewery 5 жыл бұрын

Now I understood "Fixed point iteration" very well. THANK YOU!!!

@Michael-Hammerschmidt 2 жыл бұрын

Thank you so much! My professor only every talks about these things in very general terms and never gives concrete examples. This helped me so much.

@ittein Жыл бұрын

老师，您讲解的是我在这个平台上看到的最好的讲解视频，让我彻底理解了这三个求根法，虽然在微积分中已经学过但有了新的意义。

@xingyuwang3299 2 жыл бұрын

Clear, easy to understand, detailed. A really good teacher. Thank you for uploading this video.

@_juanzu_ 4 жыл бұрын

Thanks for the videos Dr. Shen! The content is rich and really well explained. Best regards.

@kesh2032 5 жыл бұрын

Amazing !! You really know how to teach. Thanks a million

@elainelif 3 жыл бұрын

I'm doing my homework right now with the help of this video. Thank you so much!

@wenshenpsu 2 жыл бұрын

Thanks for watching!

@jiayibao6708 7 жыл бұрын

This lecture is very amazing ！！！ so clear and organized！！

@wenshenpsu 7 жыл бұрын

Thanks!

8 жыл бұрын

You are an excellent teacher, I am glad to have found your channel. Many thanks.

@wenshenpsu 8 жыл бұрын

+Márcio Laubstein I am glad to know that you appreciate these videos. Thanks.

@passer2by 4 жыл бұрын

You are many times better than my prof at school! It's 100% the same stuff but my prof makes it many times harder.

@99BeastMaker 3 жыл бұрын

This is a proper math lecture...lots of example...students are actually included in the derivation of this complete algorithm....bravo

@wenshenpsu 2 жыл бұрын

Thanks for watching and for your kind comments.

@k3nny111 8 жыл бұрын

Thank you, Dr. Shen, for providing this great lecture.

@wenshenpsu 8 жыл бұрын

+k3nny111 You are welcome! I am glad that you like it.

@jalaldjerradi Ай бұрын

you are the best no matter somtimes we can't understand every thinks

@oscarmejia8306 8 жыл бұрын

Amazing ability for teaching! Thank you so much!!

@wenshenpsu 7 жыл бұрын

Thanks!

@qilunlyu8110 4 жыл бұрын

The second example at 29:00 g'(x) should be -2e^(-2x)(x-1)+e^(-2x)+1

@user-il5nd2ez3k 7 жыл бұрын

Thank you! Your lectures are very helpful and well organized! You are a very excellent teacher!

@wenshenpsu 7 жыл бұрын

Thanks.

@wenshenpsu 6 жыл бұрын

Thanks.

@bird9 2 жыл бұрын

Waw I am impressed, such an amazing lecture ! Thank You !

@burakbulut7590 7 жыл бұрын

i wish i had a teacher like you.

@wenshenpsu 6 жыл бұрын

Thanks. There are many lectures here to watch.

@AdityaFingerstyle 6 жыл бұрын

Best explanation on Fixed Point method on KZfaq

@wenshenpsu 6 жыл бұрын

Thanks for your kind comments.

@stroxsarchive8151 2 жыл бұрын

Simply Incredible! Thanks a lot ma'am you saved my ass this semester

@tthtlc 6 жыл бұрын

I like this, better than other lectures on fixed point theorem.

@wenshenpsu 6 жыл бұрын

I am glad. Thanks for watching.

@Unknown-du4yl 3 жыл бұрын

Really Appreciable lecture, Brilliant professor

@sophiezhao5903 2 жыл бұрын

She is a good teacher ! very clairly

@anjulalakshan6524 2 жыл бұрын

you are very good in teaching.. keep it up..

@birhanubetela7373 6 жыл бұрын

the best lecture i have ever see!!! thank you so much

@wenshenpsu 5 жыл бұрын

Thanks for watching!

@salimgaoua9618 2 жыл бұрын

This video is amazing ! thank you very much

@jamirahamaahmed5197 8 жыл бұрын

you're an excellent teacher! Thanks so much.

@wenshenpsu 8 жыл бұрын

+Jamirah Ama Ahmed Thank you!

@ridwannana-yawamoako2939 6 жыл бұрын

Oh I see.

@wenshenpsu 6 жыл бұрын

Thanks!

@calvinmuchemwa3880 5 жыл бұрын

Thank you for the lecture,God Bless you

@AlbaniM 8 жыл бұрын

Thanks so much for this!, great lecture.

@wenshenpsu 8 жыл бұрын

+Manuel Albani I am happy that you like it. Thanks for watching.

@serden8804 5 жыл бұрын

you are so cute and i love your teaching style. Thanks for these amazing lectures. The world needs teachers like you :)

@Bridgelessalex 4 жыл бұрын

weird comment ....

@serden8804 4 жыл бұрын

@@Bridgelessalex why

@ihteramali827 7 жыл бұрын

the convergence or divergence of the equation defend on g(x) so how we choose a better g(x) such that we get our required result.

@hdmi00 8 жыл бұрын

Wish I had you as a teacher! Thank you!

@wenshenpsu 8 жыл бұрын

+Hadhemi Laouini Thank you!

@carolabelitado9425 2 жыл бұрын

Watching this for tommorow's final exam!

@dithopulungan2687 5 жыл бұрын

Can you please make the video about fixed-point iteration for a set of nonlinear equations? I am very interested in how the behavior of FPI on the order of the equations? I mean, which equations need to solve first? will it make any difference if I solve certain equation first compare to other equation? I hope you catch my question. Thanks

@tildarusso Жыл бұрын

极好的巴那赫不动点定理的讲解！

@manas1743 3 жыл бұрын

Thanks for the lecture and video ,you teach really well. Cleared all my doubts regarding the method.

@wenshenpsu 2 жыл бұрын

You are most welcome!

@evenderatusayemkili3280 Жыл бұрын

You are so amazing,,,, fixed point iteration was a big problem to me, hope you were my mom😂

@AJ-et3vf 2 жыл бұрын

Thank you so much foe this lecture maam. Very helpful!

@the195 5 жыл бұрын

Very lovely video. Can you just explain the proof of convergence using Taylor's theorem, please?

@YouTubeChannel2000 8 жыл бұрын

Is there a way to get to the root faster by averaging the points of the spiral shape, which results when there is a negative slop around the root point?

@wenshenpsu 8 жыл бұрын

+W. Al-Rikabi Fixed point iteration is not a fast method, since it only has linear convergence. Newton iteration is much faster, and some combination of them would work very well. Try watch some other videos here! Thanks!

@wsrabbit6699 7 жыл бұрын

Appreciated! thank you, you took me from failing to flying!!!! appreciated thanks allot!

@wenshenpsu 6 жыл бұрын

Great to hear that!

@david.v7605 3 жыл бұрын

@@wenshenpsu cosine 1 is 0.999 how did you get 0.54?

@Nikhil-eo4xj 8 жыл бұрын

Awesome videos!!! Thank you so much

@wenshenpsu 7 жыл бұрын

Thanks for watching.

@ihteramali827 7 жыл бұрын

i m very thank full to Mad'm wenshenpsu for explaining this method such in a easy way i understand it very well and i hope other people will also understand it..

@wenshenpsu 7 жыл бұрын

Thank you!

@codmix 7 жыл бұрын

how can i calculate x1 in example 1 in matlab or in science calculator to find right answer and thanks for vedio doctor

@janghwanim5750 6 жыл бұрын

Thanks for your beautiful lecture!

@wenshenpsu 6 жыл бұрын

Thanks for watching.

@saheedadisa8077 Жыл бұрын

I feel like this video shouldn't end :)

@phathutshedzomaungo596 9 жыл бұрын

Very clear and concise. Thank you

@wenshenpsu 8 жыл бұрын

+PHATHUTSHEDZO MAUNGO Thanks!

@wenshenpsu 6 жыл бұрын

Thanks.

@tekiletefera2783 2 жыл бұрын

nice teacher keep it up thank you

@LukeBockman 8 жыл бұрын

-The derivative at 28:17 is wrong. -It should be g'(x) = -2x*exp(-2x)+3*exp(-2x)+1. -It doesnt change her conclusion from pluggin in g'(1) = exp(-2)+1 though.

@LukeBockman 8 жыл бұрын

+K. Macarena Antonio ......maybe check your math again. pretty sure I'm right.

@wenshenpsu 8 жыл бұрын

+Luke Bockman Sharp eyesight! Yes, the last term should be 1, as you indicated. Sorry for the typo, and keep up your sharp eyesight!

@mariaceciliaargibay88 9 жыл бұрын

thank you! it was really clear and easy to follow

@wenshenpsu 8 жыл бұрын

+Cecilia Argibay Thanks!

@wenshenpsu 6 жыл бұрын

Thanks!

@Mr._Y2666 Жыл бұрын

So clear!!!!!!

@matiassantacruz5487 2 ай бұрын

Great video! One small mistake though at 20:37, you are actually using the Mean Value Theorem, not the Intermediate Value Theorem.

@birhanubetela7373 6 жыл бұрын

how can I get the free download of this video

@islamelbaz7232 8 жыл бұрын

Wonderful, thank you doctor

@wenshenpsu 8 жыл бұрын

You are welcome!

@kiranboddeda4121 2 жыл бұрын

The wrong choice of g(x) is leading us to a divergence ...can we just solve for x and can we proceed with the procedure which have enforced in example 1 ?

@cgafa 3 жыл бұрын

Is it the Intermediate Value Theorem or the Mean Value Theorem? 20:38

@onlyawesome4864 5 жыл бұрын

Great video Iv ever seen on this topic.👍👌💐 BTW Is your student is your cameraman?😊

@wenshenpsu 5 жыл бұрын

Thanks for watching! It's recorded by a video technician.

@EmapMe 6 жыл бұрын

20:50 i don't get how you got that bottom expression?

@HanzAlbertNguyen 6 жыл бұрын

man, this is very clear

@wenshenpsu 6 жыл бұрын

Thanks.

@abdeldjabardaoud503 6 жыл бұрын

i not good in english but i understood this method Thanks to you

@wenshenpsu 6 жыл бұрын

Thanks! Enjoy the classes.

@salmahoussaini1710 5 жыл бұрын

Hello, thank you for your very useful video, just I had a problem to understand how you used the Intermediate Values Theorem (in 20:47 of the video), because what I know is that theorem gives us just the existence: when we have an element u between g(Xk) and g(r) there existe an element c between Xk and r such that g(c) = u . I think you wanted to say Mean Value Theorem.

@lilkamal8607 4 жыл бұрын

i also think so

@sisayfk6546 Жыл бұрын

Thanks

@saifraaed7834 7 жыл бұрын

that was amazing . thank you alot

@wenshenpsu 7 жыл бұрын

Thanks.

@isaacowusuansah172 6 жыл бұрын

how do you chose your guess x when you have not been given that or your interval

@wenshenpsu 6 жыл бұрын

There are sampling procedure that searches for a good initial guess, but it's out of the scope of this course.

@ireneisme8747 4 жыл бұрын

20:40 Could someone kindly explain this step?

@arbitrarilyarbitrary8440 4 жыл бұрын

Irene ZHAO This is a specific case of something called the intermediate value theorem. It states that if f(x) is differentiable on some interval (a,b) and continuous on [a,b] then there exists some value c in [a,b] such that (f(b)-f(a))/(b-a)=f’(c). In other words, there exists some value for c in the interval [a,b] such that the slope of the graph at c is equal to the average change in f(x) on the interval [a,b]. Now the lecturer in this video made use of the fact that if (f(b)-f(a))/(b-a)=f’(c) then f(b)-f(a)=f’(c)(b-a) (basic algebra). So, if we have some number x(k+1) being an iteration of g(x(k)) then x(k+1)=g(x(k)) and r=g(r). From there she states that for some value c or that weird Greek letter must then satisfy the the conditions of the intermediate theorem, namely that f(b)-f(a)=f’(c)(b-a) only now b=x(k) and a=r such that f(x(k))-f(r)=f’(c)(x(k)-r). Note that in the equation shown in the video absolute stripes are used. However it is not hard to see that if f(x(k))-f(r)=f’(c)(x(k)-r), |f(x(k))-f(r)|=|f’(c)(x(k)-r)| also applies. I hope this clears it up for you. If not I highly recommend watching a quick video on the intermediate value theorem and then coming back to this video to see if it all makes sense.

@Youlix16 7 жыл бұрын

Good morning miss wen! i saw your video avout fixed point method and it was amazing , thanks a lot ! but i have a problem with one exemple i have x=1+1/x+1/x² , where g(x)=1+1/x+1/x² the max l g'(x) l =3 which is > 1 so the fixed point method shouldn't work , i plugged it in matlab and it works ..... how is that even possible?

@nishantsaini2946 8 жыл бұрын

whats the difference between what you taught and the contraction mapping theorem?

@wenshenpsu 7 жыл бұрын

If the fixed point iteration is contractive, then the iteration will converge.

@halkoumahmed3430 7 жыл бұрын

hi, I've noticed in french books that they add another condition to the function g(x)to guarantee the convergence which is g([a,b]) included in (a,b),is that not interesting . thank you for your method of teaching that was amazing lecture

@wenshenpsu 7 жыл бұрын

That condition will guarantee the existence of a fixed point on the interval [a,b].

@wordenx2199 2 жыл бұрын

Thank ms🌹

@emmanuelchikeluba2360 4 жыл бұрын

In the first example you solved: f(x) = x-cosx You did not add x to both sides as you indicated in your introduction to this topic.

@purnendrasinghrajput8848 4 жыл бұрын

Guy below is right 'even my iit teachers didn't taught so well

@Adam_mohammed_ Жыл бұрын

The book is in front of me… looking at slides already… trying to understand from the book…but I am still lost!! What is the point of this lesson!? And what do the examples of this lesson look like!?

@fakheriqbal3817 7 жыл бұрын

Great Teaching

@wenshenpsu 7 жыл бұрын

Thanks.

@ghulamhabib948 8 жыл бұрын

how can we first select x0 and g(x)

@hdmi00 8 жыл бұрын

+Ghulam Habib x0 is a "guess" if you know the root "r" choose close to it, as for g(x) is actually f(x)+x, you take your initial function and you add x to both sides.

@XpressCrosSs 7 жыл бұрын

thank you a lot

@wenshenpsu 7 жыл бұрын

Thanks for watching.

@user-mi1us1pf8t 5 жыл бұрын

Thanks but l think you mistake in g derivative at times 28

@aijazahmaddar7437 8 жыл бұрын

Mam please replace lecture on error propagation by new one as vedio image is not clear

@wenshenpsu 8 жыл бұрын

Sorry for that. They did not use an HD camera for that recording. You can find the power point lectures on this topic in my channel as well. Try them.

@bjg4320 7 жыл бұрын

Can I ask a question? If I find a g(x) is divergence, do I need to use anther way to find anther g(x). For example, I use f(x) + x = g(x), but this g(x) is divergence, can I use newton find anthor g(x) = x - f(x)/f`(x)

@bjg4320 7 жыл бұрын

Is any possible different g(x) get opposite ans

@wenshenpsu 7 жыл бұрын

Yes there are many ways of making g(x). In fact, you watch more videos, the Newton iteration will be covered, and it can be viewed as the "best" choice of g(x).

@bjg4320 7 жыл бұрын

Thank you so much

@rickmonarch4552 4 жыл бұрын

dafuq, I understand. :O U r my heroine. Nanananana WenShen!!!! :D

@chathurawimalasiri5920 2 жыл бұрын

what happen if abs( g`(x) ) = 1 ?

@aymenechchalim4654 Жыл бұрын

in case somebody else makes the same remark, it still does not work, the error stays stagnated e(k+1)=1.e(k), while we want it to decrease after each iteration executed.

@aezkimo5366 9 жыл бұрын

hello please How do we choose the right first estimation x0????

@wenshenpsu 9 жыл бұрын

aez kimo You may use a couple of bisections steps to generate a good x0.

@wenshenpsu 8 жыл бұрын

+aez kimo You need to use an x0 such that it satisfies the conditions in the Convergence Theorem. Usually this is not easy to find, it is more a guess-and-try procedure. One possible way is to use a hybrid method: first use bisection method to find a value that is close to the root, then use it as x0 to perform the fixed point iteration (or Newton iteration, which is much faster). Hope this helps!

@anzelnel9586 4 жыл бұрын

7:15 it says "Fuck" on the board

@the_informative_edge 3 жыл бұрын

Respectable professor in example 2 you have used g(x)=f(x)+x, when f(x)=0. Where as in example f(x)# 0.

@abdiborutube9151 7 жыл бұрын

it is fine

@wenshenpsu 7 жыл бұрын

Thanks.

@ahmedabdi2275 7 жыл бұрын

Thank yoooooooooooou sooooo muuuuuuuuuuuch

@wenshenpsu 7 жыл бұрын

You are welcome.

@wenshenpsu 6 жыл бұрын

Thanks.

@marflage 4 жыл бұрын

I can not understand. The sound is not audible. I really wanna watch this video as the reviews are all positive :(

@supunsenanayake1952 6 жыл бұрын

excellent

@wenshenpsu 6 жыл бұрын

Thanks.

@Arch_Circle 7 жыл бұрын

Awesome

@wenshenpsu 7 жыл бұрын

Thanks.

@Chrismbo 8 жыл бұрын

at 12:12 why did she add x on both sides?, why not just start iteration with f(x) = exp-2x(x-1)? OR if she added x to make it subject of formula, by equating exp-2x(x-1) + x = 0, why wasn't the iteration x = -exp-2x (x-1)?

@wenshenpsu 8 жыл бұрын

+Chris B Adding an x to both sides of f(x)=0 makes it a fixed point for x=f(x)+x=g(x). Hope this explains.

@Chrismbo 8 жыл бұрын

+wenshenpsu Thanks, that helps.

@emmanuelchikeluba2360 4 жыл бұрын

But that x was not added on both sides in the first example you solved madam. f(x) = x-cosx=0

@Arch_Circle 7 жыл бұрын

28:08 >> update +x to +1

@wenshenpsu 7 жыл бұрын

Yes thanks. I will add an annotation.

@hakchoi100 9 жыл бұрын

It is computer course! Nothing about the fixed point theorem.

@wenshenpsu 8 жыл бұрын

+Choi Hak Yes, it's on numerical methods.

@zairoxs 5 жыл бұрын

I am deaf on my left ear so I could not hear the video; KZfaq should implement a button to switch audio channels. If only there was right ear audio...