CMPSC/Math 451: March 2, 2015. Fixed point iterations. Wen Shen

[@essafr3823]

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.

[@tt6-2-76]

insane glazing

[@edwincuevas9965]

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

[@ittein]

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。

[@loloioi]

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

[@wenshenpsu]

Thanks!

[@99BeastMaker]

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

[@wenshenpsu]

Thanks for watching and for your kind comments.

[@Michael-Hammerschmidt]

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.

[@CharlieLyu868]

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

[@binni8507]

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

[@elainelif]

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

[@wenshenpsu]

Thanks for watching!

[@jiayibao6708]

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

[@wenshenpsu]

Thanks!

[@xingyuwang3299]

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

[@burakbulut7590]

i wish i had a teacher like you.

[@wenshenpsu]

Thanks. There are many lectures here to watch.

[@LukeBockman]

-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]

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

[@wenshenpsu]

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

[@jalaldjerradi]

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

[@kesh2032]

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

[@passer2by]

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

[@杰米老师]

you're an excellent teacher! Thanks so much.

[@wenshenpsu]

+Jamirah Ama Ahmed Thank you!

[@ridwannana-yawamoako2939]

Oh I see.

[@wenshenpsu]

Thanks!

[@AdityaFingerstyle]

Best explanation on Fixed Point method on KZbin

[@wenshenpsu]

Thanks for your kind comments.

[@k3nny111]

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

[@wenshenpsu]

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

[@Mare_brewery]

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

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

[@wenshenpsu]

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

[@ihteramali827]

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]

Thank you!

[@manas1743]

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

[@wenshenpsu]

You are most welcome!

[@tthtlc]

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

[@wenshenpsu]

I am glad. Thanks for watching.

[@东方不败-n2e]

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

[@wenshenpsu]

Thanks.

[@wenshenpsu]

Thanks.

[@_juanzu_]

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

[@dithopulungan2687]

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

[@sophiezhao5903]

She is a good teacher ! very clairly

[@oscarmejia8306]

Amazing ability for teaching! Thank you so much!!

[@wenshenpsu]

Thanks!

[@phathutshedzomaungo596]

Very clear and concise. Thank you

[@wenshenpsu]

+PHATHUTSHEDZO MAUNGO Thanks!

[@wenshenpsu]

Thanks.

[@anjulalakshan6524]

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

[@serden8804]

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

[@Bridgelessalex]

weird comment ....

[@serden8804]

@@Bridgelessalex why

[@stroxsarchive8151]

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

[@matiassantacruz5487]

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

[@salmahoussaini1710]

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]

i also think so

[@carolabelitado9425]

Watching this for tommorow's final exam!

[@the_informative_edge]

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

[@Unknown-du4yl]

Really Appreciable lecture, Brilliant professor

[@the195]

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

[@emmanuelchikeluba2360]

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.

[@bird9]

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

[@AJ-et3vf]

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

[@hdmi00]

Wish I had you as a teacher! Thank you!

[@wenshenpsu]

+Hadhemi Laouini Thank you!

[@tildarusso]

极好的巴那赫不动点定理的讲解！

[@birhanubetela7373]

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

[@wenshenpsu]

Thanks for watching!

[@kiranboddeda4121]

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 ?

[@AlbaniM]

Thanks so much for this!, great lecture.

[@wenshenpsu]

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

[@evenderatusayemkili3280]

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

[@abdeldjabardaoud503]

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

[@wenshenpsu]

Thanks! Enjoy the classes.

[@salimgaoua9618]

This video is amazing ! thank you very much

[@halkoumahmed3430]

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]

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

[@ihteramali827]

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.

[@calvinmuchemwa3880]

Thank you for the lecture,God Bless you

[@cgafa]

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

[@wsrabbit6699]

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

[@wenshenpsu]

Great to hear that!

[@david.v7605]

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

[@janghwanim5750]

Thanks for your beautiful lecture!

[@wenshenpsu]

Thanks for watching.

[@mariaceciliaargibay88]

thank you! it was really clear and easy to follow

[@wenshenpsu]

+Cecilia Argibay Thanks!

[@wenshenpsu]

Thanks!

[@onlyawesome4864]

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

[@wenshenpsu]

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

[@saheedadisa8077]

I feel like this video shouldn't end :)

[@purnendrasinghrajput8848]

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

[@tekiletefera2783]

nice teacher keep it up thank you

[@HanzAlbertNguyen]

man, this is very clear

[@wenshenpsu]

Thanks.

[@Youlix16]

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?

[@Nikhil-eo4xj]

Awesome videos!!! Thank you so much

[@wenshenpsu]

Thanks for watching.

[@sachinpundir6185]

Nice Explanation

[@codmix]

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

[@YouTubeChannel2000]

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]

+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!

[@Adam_mohammed_]

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!?

[@marflage]

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

[@islamelbaz7232]

Wonderful, thank you doctor

[@wenshenpsu]

You are welcome!

[@Chrismbo]

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]

+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]

+wenshenpsu Thanks, that helps.

[@emmanuelchikeluba2360]

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

[@EmapMe]

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

[@fakheriqbal3817]

Great Teaching

[@wenshenpsu]

Thanks.

[@واثقابوموسىالاسدي]

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

[@birhanubetela7373]

how can I get the free download of this video

[@nishantsaini2946]

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

[@wenshenpsu]

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

[@Mr._Y2666]

So clear!!!!!!

[@isaacowusuansah172]

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

[@wenshenpsu]

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

[@bjg4320]

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]

Is any possible different g(x) get opposite ans

[@wenshenpsu]

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]

Thank you so much

[@aijazahmaddar7437]

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

[@wenshenpsu]

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.

[@saifraaed7834]

that was amazing . thank you alot

[@wenshenpsu]

Thanks.

[@wordenx2199]

Thank ms🌹

[@aezkimo5366]

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

[@wenshenpsu]

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

[@wenshenpsu]

+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!

[@sisayfk6546]

Thanks

[@ireneisme8747]

20:40 Could someone kindly explain this step?

[@arbitrarilyarbitrary8440]

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.

[@chathurawimalasiri5920]

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

[@aymenechchalim4654]

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.

[@anzelnel9586]

7:15 it says "Fuck" on the board

[@ghulamhabib948]

how can we first select x0 and g(x)

[@hdmi00]

+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.

[@hakchoi100]

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

[@wenshenpsu]

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

[@ahmedabdi2275]

Thank yoooooooooooou sooooo muuuuuuuuuuuch

[@wenshenpsu]

You are welcome.

[@wenshenpsu]

Thanks.

[@XpressCrosSs]

thank you a lot

[@wenshenpsu]

Thanks for watching.

[@rickmonarch4552]

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

[@supunsenanayake1952]

excellent

[@wenshenpsu]

Thanks.

[@Arch_Circle]

28:08 >> update +x to +1

[@wenshenpsu]

Yes thanks. I will add an annotation.

[@Arch_Circle]

Awesome

[@wenshenpsu]

Thanks.

[@abdiborutube9151]

it is fine

[@wenshenpsu]

Thanks.

[@zairoxs]

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

[@heddikaddouri7709]

can I ask a question

[@deephish]

someone should tell her its pronouced err+or not err+ow