Newton's method for solving nonlinear systems of Algebraic equations

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The Math Guy

6 жыл бұрын

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

Пікірлер: 101

@ABM30100 3 жыл бұрын

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!

@lukasmo7439 4 жыл бұрын

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

@the-Math-guy 4 жыл бұрын

You are correct it was a typo from my notes.

@sharpnova2 3 жыл бұрын

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

@tumurtumur3101 3 жыл бұрын

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

@sofiaaylan483 2 жыл бұрын

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

@yassinghareeb5761 2 жыл бұрын

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

@markbanash921 Жыл бұрын

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

@MathewsDozola-ce2hv 10 ай бұрын

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

@chawnneal3103 2 жыл бұрын

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!

@ibrahimallafi1460 3 жыл бұрын

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

@0mon0zz 3 жыл бұрын

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

@DXenakis 4 жыл бұрын

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?

@rond5936 4 жыл бұрын

Really good explanation. Thank you, Math Guy.

@davidcolomer941 3 жыл бұрын

Thanks a lot professor Guy, very helpful

@devingauthier2933 2 жыл бұрын

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

@MM-bn7uo 4 жыл бұрын

very usefull method and with good explanation thank you so much

@Stagnum_404 3 ай бұрын

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 🫶

@jithinpoliyedathmohanan7237 4 жыл бұрын

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

@TheChodex 6 жыл бұрын

Thanks for this video man! :D

@thomashietala3815 Жыл бұрын

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?

@matitiudeforever8155 5 жыл бұрын

thanks a lot man !! it really really helped me

@wraster07hp36 3 жыл бұрын

Very good presentation, thanks Mr.

@tanvirkaisar7245 Жыл бұрын

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

@TheValli28 6 жыл бұрын

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 6 жыл бұрын

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.

@gyanapriyadarshi 8 ай бұрын

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

@azhankhan9218 Жыл бұрын

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

@s.ichannel9331 11 ай бұрын

Right 😅

@tabhashim3887 3 жыл бұрын

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

@divibedivide 3 жыл бұрын

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

@mitchieroa2164 4 жыл бұрын

thanks to this! helped me a lot

@peiyanyang3612 2 жыл бұрын

Excellent video!!! Clear explain!

@anassalammiri340 4 жыл бұрын

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

@tobiasgorgen7592 3 жыл бұрын

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

@nvk-aggie 4 ай бұрын

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).

@andre.queiroz 3 жыл бұрын

Thanks! Helped a lot!

@eldritch2300 Жыл бұрын

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 Жыл бұрын

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 11 ай бұрын

@@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 4 ай бұрын

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

@bobasawrus 9 ай бұрын

Thankyou for your very clear explanation!

@ponegikekana8786 Жыл бұрын

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

@madinaotkel6549 4 жыл бұрын

Could you explain why it's n^3

@hassanmunir7971 2 жыл бұрын

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

@anassalammiri340 4 жыл бұрын

Thank you!

@sagarmehla3781 3 жыл бұрын

You are awesome.

@xruan6582 4 жыл бұрын

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 4 жыл бұрын

@jome8059 3 жыл бұрын

you are right. I was thinking the same

@stringsam 3 жыл бұрын

amazing explanation

@MST-ul7ol 2 жыл бұрын

Thanks a lot for this content

@Skeeter666666 6 жыл бұрын

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 6 жыл бұрын

Great overall video though!

@the-Math-guy 6 жыл бұрын

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

@adityabodhe3340 3 жыл бұрын

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 3 жыл бұрын

Elementary Linear Algebra by Howard Anton.

@adityabodhe3340 3 жыл бұрын

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

@omidabachian5369 24 күн бұрын

Fantastic

@rameztabar2186 4 ай бұрын

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

@santoshkumarsahani5289 2 жыл бұрын

Thank you so much... ❤️

@jaswantkumar8387 3 жыл бұрын

What will happen when inverse of Jacobian is 0

@karoleus1208 3 жыл бұрын

Kudos!

@ChitralPatil Жыл бұрын

excellent!

@erwinbernardiitalento283 3 жыл бұрын

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

@ahmedmoustafa5043 3 жыл бұрын

same

@akauppi2 3 жыл бұрын

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

@wahabmustafa7360 3 жыл бұрын

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

@ador4047 4 жыл бұрын

How did u choose the initial guess? Just random?

@the-Math-guy 4 жыл бұрын

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

@ador4047 4 жыл бұрын

@@the-Math-guy thanks ♥️

@ahmetkarakartal9563 2 жыл бұрын

thank you so much

@TripedalTroductions 4 жыл бұрын

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

@omarali-rv3ht 4 жыл бұрын

true

@josecarlosferreira4942 2 жыл бұрын

Old (not so much), but Gold!

@nadmaanfazeel2691 2 жыл бұрын

how to find initial guess

@siddharthsinghkiryal2082 2 жыл бұрын

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

@souravyaduvanshi6900 6 жыл бұрын

How we take initial guess

@the-Math-guy 6 жыл бұрын

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

@user-nm3qz3bs2k 5 жыл бұрын

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

@gagansarswa8331 3 жыл бұрын

Thanks sir !!

@gagansarswa8331 3 жыл бұрын

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

@divyabachda555 Жыл бұрын

Hello sir , Can I get this PPT ?

@the-Math-guy Жыл бұрын

I'm sorry I don't have any ppts

@nokubongamntombi8068 3 жыл бұрын

Isn't X-y=7 ?linear

@riderwalker3099 5 жыл бұрын

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 5 жыл бұрын

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 5 жыл бұрын

@@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 5 жыл бұрын

@@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