Newton's method for solving nonlinear systems of Algebraic equations

In this video we are going to how we can adapt Newton's method to solve systems of nonlinear algebraic equations.

[@ABM30100]

At times, I stress out about not understanding concepts in lectures. Then I remember this is the best period to be learning anything. Thousands of talented people offering free content with explanations and examples to help you understand - irrespective of how good / bad your lecturer at uni is. This video was very helpful. Thank you very much!

[@yassinghareeb5761]

Can't thank you enough for this, exam is in few hours and all my friends are asleep. Big help, appreciate it.

[@MathewsDozola-ce2hv]

You really helped me during my university studies more especially in Numerical Analysis. 🔥🔥🔥

[@lukasmo7439]

just a little mistake: in minute 15:13 there must be a (minus 7/12) instead of 7/12

[@the-Math-guy]

You are correct it was a typo from my notes.

[@sharpnova2]

@@the-Math-guy I followed along with your work but did the calculations myself so I got worried. Thankful for this comment.

[@tumurtumur3101]

in minute 16:18 there must be a (minus 1.67) instead of 1.67???

[@sofiaaylan483]

si es -7/12 jajaja yo estaba haciendo el gauss como 3 veces

[@chawnneal3103]

Thanks a ton, Math Guy! Probably similar to most people, I got a zoom class prof with bad audio and this class doesn't follow a textbook sadly. So y'all here are heroes!

[@markbanash921]

Thank you! I did this in graduate school but had forgotten all about it. Excellent and applicable refresher.

[@nvk-aggie]

Great video! As a note, If we change the initial guess values to (1.0; 0.0) we obtain a different final solution as (2.0; 0.0).

[@0mon0zz]

Great video! There's a few arithmetic mistakes but the content is GOLD. Thank you soooo much for sharing! :)))

[@gyanapriyadarshi]

Thank God. At least someone explained it clearly. Thank you.

[@azhankhan9218]

At 15:10 it should be -7/12 By the way addictive videos 👍.

[@s.ichannel9331]

Right 😅

[@Stagnum_404]

Man, you’re so good at explaining. I really appreciate the real example instead of a generic one, it helps a lot. I’m currently writing by bachelor thesis using the newtons method in n dimensions couldn’t understand how to calculate the Jacobian. This video helped me a lot. Thanks for your expertise 🫶

[@eldritch2300]

Could you please explain how the gaussian elimination works once you get to J*delta = -F. I can't find anywhere online that explains how to solve it for Newton's.

[@setsu2221]

Wolframalpha format would be: [{1, 2},{2, 16}] * [{x},{y}] = [{-3}, {-13}] where x = x_1, and y = x_2 As you may have noticed, there is also an error at 14:28, as both of the variables are supposed to be negative. Gaussian elimination would be something along the lines of: 1 2 | -3 2 16 | -13 Swap R1 and R2 2 16 | -13 1 2 | -3 Subtract 1/2 * R1 from R2 2 16 | -13 0 -6 | 7/2 Multiply R2*2 2 16 | -13 0 -12 | 7 Divide R2 by -12 2 16 | -13 0 1 | -7/12 Subtract 16*R2 from R1 2 0 | -(11/3) 0 1 | -(7/12) Divide R1 by 2 1 0 | -(11/6) 0 1 | -(7/12) Then you can easily read (from the left-hand-side matrix) that: x_1 = -11/6 x_2 = -7/12 Does that sufficiently answer your comment?

[@sanjitsounderrajan]

@@setsu2221That is what I got when I solved by hand, however at 14:26 the video shows x_2 = 7/12. Where did the -ve sign go?

[@luisv8887]

@@setsu2221 thank you i thought i was dumb and got it wrong! but i got the same as you! thanks!

[@tabhashim3887]

wouldn't using gaussian elimination be just as much computation as using the inverse in the first place??

[@TheValli28]

At around minute 5, when you re-introduce Newton's method and connect it with the vectors you just introduced earlier, you are using the wrong denotations for the time-steps. You're using n as an indication for the current time-step, whereas the equations you're using later are using k. This also creates some confusion as the vector-elements in x and f(x) are denoted with n. Good video though. It helped.

[@the-Math-guy]

Thank you for pointing that our but it was not in error its just the way I started and then converted the scalar to the vector. Please follow the k-version that is the clear one and you are right it should not have been n as they don't have to be the same counters in any case.

[@anassalammiri340]

What are the conditions on the initial guess. It's not random. In some cases the sequence won't converge.

[@tobiasgorgen7592]

If you have sufficiently "nice" functions you can make a first estimate. For example by estimating your function via a powerseries with p = 1/2. That way you can get a arbitrarily close number (by ineffective means o/c) to use as a starting point

[@davidcolomer941]

Thanks a lot professor Guy, very helpful

[@divibedivide]

13:17 shouldn't it be 64 instead of 16? Cuz you have x sub 2 squared and the value of x sub 2 is 2

[@HoangM-zi7uk]

thank you very much for this very helpful video

[@jithinpoliyedathmohanan7237]

Super viedio man keep it up.. Mach weiter so...❤️❤️❤️

[@xruan6582]

it is confusing to use 'n' to represent both the size of x vector and the time steps in newton's method

[@the-Math-guy]

Thank you for pointing that our but it was not in error its just the way I started and then converted the scalar to the vector. Please follow the k-version that is the clear one and you are right it should not have been n as they don't have to be the same counters in any case.

[@jome8059]

you are right. I was thinking the same

[@omidabachian5369]

Fantastic

[@AymanFakri-ou8ro]

thanks! very clear explanation!

[@ibrahimallafi1460]

Thank you so much, but I have a question. What do we have to do if the delta of the Jacobian matrix is zero?

[@devingauthier2933]

Used this stuff to solve a tricky problem at work. Thanks!

[@rond5936]

Really good explanation. Thank you, Math Guy.

[@hassanmunir7971]

I don't understand how you used Guess method here. I was specifically looking for this point which you wrote directly.

[@adityabodhe3340]

thanks for a very insightful video. please suggest me a book for studying this part of algebra. thanks. New to this chapter and doing some self study. thank you :)

[@the-Math-guy]

Elementary Linear Algebra by Howard Anton.

[@adityabodhe3340]

@@the-Math-guy thank you so much (y)

[@erwinbernardiitalento283]

I got lost on the Gaussian Elimination part. Can some help me understand it?

[@ahmedmoustafa5043]

same

[@akauppi2]

Me, third. The Wikipedia page described it well - it’s really simple.

[@matitiudeforever8155]

thanks a lot man !! it really really helped me

[@rameztabar2186]

How will I know the final answer? after how many iterations?

[@bobasawrus]

Thankyou for your very clear explanation!

[@MM-bn7uo]

very usefull method and with good explanation thank you so much

[@tanvirkaisar7245]

Great video! I have a question, what if we had n variables but just one equation, would this method work?

[@TheChodex]

Thanks for this video man! :D

[@peiyanyang3612]

Excellent video!!! Clear explain!

[@ponegikekana8786]

at 16.20 min in the vid , is'nt 1.67 suppose to be a negative? since we are multiplying -10/12 by 2?

[@wraster07hp36]

Very good presentation, thanks Mr.

[@TripedalTroductions]

This video is pretty old but given x0 =(1,2) x1 should be (-5/6,17/12)

[@omarali-rv3ht]

true

[@wahabmustafa7360]

in jacobian matrix there are mistakes in Subscripts... Kindly check it

[@stringsam]

amazing explanation

[@sagarmehla3781]

You are awesome.

[@thomashietala3815]

Hi, I'm having some problems applying Newton's method, as it won't converge.The problem that I have is that the relative difference between succesive iterations is always quite big... (always above 5%), so I can never really stop the iterative process. I think in part it is because the values that I use in the F matrix can be very large or very small, but is there some other way of fixing/avoiding this problem?

[@andre.queiroz]

Thanks! Helped a lot!

[@riderwalker3099]

15:39 you added 7/12+2 and wrote 17/12 is that true??? i mean 7/12)+24/12=31/12

[@the-Math-guy]

Oh my goodness you are absolutely right. You know those are notes from the class I took as an undergrad. The printed stuff is from that. My apologies but the method is correct.

[@riderwalker3099]

@@the-Math-guy yeah, thanks for replying i was questioning myself. but thanks you just helped me yesterday just 4 hours before deadline when i was having tough schedule thanks a lot

[@kfernando1ify]

@@the-Math-guy Hey yeah, I think it should be (-)7/12 + 2 which is equal to 17/12, just missing a negative sign while doing it all g

[@DXenakis]

Would this method work for overdetermined systems of non-linear equations where there is no single solution? e.g. to optimize/find some best solution?

[@RiverSchreckengost-g6m]

13:23 error with the 16 plugging into the original 2nd equation.

[@mitchieroa2164]

thanks to this! helped me a lot

[@MST-ul7ol]

Thanks a lot for this content

[@jaswantkumar8387]

What will happen when inverse of Jacobian is 0

[@Skeeter666666]

Probably have to brush up a bit on my linear algebra rules but how did you calculate deltaX? Did you multiply both sides by the inverse of the matrix?

[@Skeeter666666]

Great overall video though!

[@the-Math-guy]

Thanks for the positive feedback. In answer to your question. Actually we calculate delta x by Gaussian elimination then we use delta x = x1-x0 or rather x1=delta x + x0 which gives us the new iterate and then we just repeat the whole thing with x1 to find x2

[@ChitralPatil]

excellent!

[@karoleus1208]

Kudos!

[@ador4047]

How did u choose the initial guess? Just random?

[@the-Math-guy]

Yes it is but from an exam point of view it might be provided in the question.

[@ador4047]

@@the-Math-guy thanks ♥️

[@anassalammiri340]

Thank you!

[@madinaotkel6549]

Could you explain why it's n^3

[@nokubongamntombi8068]

Isn't X-y=7 ?linear

[@nadmaanfazeel2691]

how to find initial guess

[@santoshkumarsahani5289]

Thank you so much... ❤️

[@divyabachda555]

Hello sir , Can I get this PPT ?

[@the-Math-guy]

I'm sorry I don't have any ppts

[@josecarlosferreira4942]

Old (not so much), but Gold!

[@ahmetkarakartal9563]

thank you so much

[@siddharthsinghkiryal2082]

Helped me in a very stressfull situation, here's your like and subscribe :)

[@irfanmauludin398]

I felt this equation just like Kalman Filter 🤭🙏

[@gagansarswa8331]

Thanks sir !!

[@gagansarswa8331]

Sir if you are really here now ,can you send me pdf copy of this presentation ?!!! Please sir if you can.

[@souravyaduvanshi6900]

How we take initial guess

[@the-Math-guy]

You can take anything its a guess so in the example above i use [1 2] you can use [0 0] anything will work.

[@الأستاذصباحالأسدي-ر1ف]

Thank you for this video , can you help me, I need the code for solving this system in matlab

[@wafflescripter9051]

I hate to bring it to 70 comments

[@abdou3966]

i love you

[@chizhang3263]

go to 2:33 for a good laugh

[@mathematical_fun_with_Sumbel]

Sir plz make the matlb code for this prossed too

[@syedtayibah4463]

Sir plz jacobian matrix R^n to R^n sent karo but hindi main

[@javiereguez]

my initial guess X0 depends on something or could be any random number? thank you for the feedback

[@akhilade-qq7xf]

wrong method

[@the-Math-guy]

Excuse me on what basis do you claim its wrong