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.

[ABM]

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!

[yassinghareeb]

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

[lukasmo]

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

[MathewsDozola-cehv]

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

[eldritch]

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.

[markbanash]

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

[tabhashim]

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

[Stagnum_]

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 🫶

[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).

[chawnneal]

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!

[anassalammiri]

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

[ibrahimallafi]

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

[azhankhan]

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

[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

[ponegikekana]

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

[adityabodhe]

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 :)

[gyanapriyadarshi]

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

[tanvirkaisar]

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

[TheValli]

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.

[thomashietala]

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?