Convergence of Newton's Method | Lecture 17 | Numerical Methods for Engineers

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Күн бұрын

Calculation of the order of convergence of Newton's method.
Join me on Coursera: imp.i384100.net/mathematics-f...
Lecture notes at www.math.ust.hk/~machas/numeri...
Paperback at www.amazon.com/Numerical-Meth...
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Пікірлер: 29

@flaguser4196 2 жыл бұрын

Textbooks should probably stop using "it's easy to show" but instead use "Taylor series expand like a madman" where applicable.

@calberk1737 3 жыл бұрын

How did you get that expression for epsilon n+1 in terms of epsilon

@subhashpaudel246 2 жыл бұрын

Root minus solution at n+1th will be error at n+1th

@agnichatian 2 жыл бұрын

Could someone give an explanation of "lifting the denominator" ?

@ProfJeffreyChasnov 2 жыл бұрын

Taylor series expansion of 1/(1-epsilon) around epsilon=0.

@chawnneal3103 2 жыл бұрын

ohhh okayy! So you did: numerator/denominator . Then numerator * (1/denominator) 1/denominator = (1/1-epsilon) ~= 1/(1-x) taylor of 1/(1-x) = 1+x

@6Scarfy99 Жыл бұрын

@@chawnneal3103 yes

@arthurlau2020 2 жыл бұрын

in 6:19, you lift up the denominator, how did it happen?

@ProfJeffreyChasnov 2 жыл бұрын

Taylor series expansion

@arthurlau2020 2 жыл бұрын

wiki describes Newton's method a little differently, And I am confused. wiki says X(n+1) = X(n) - (first derivative of f)/(second derivative of f), it also uses talyor series to come up with the method. Is there any difference between these two method, although they are both called newton's method. thank you for your help

@arthurlau2020 2 жыл бұрын

Is the newton's method for solving the equations, and the one I mentioned above is for the optimization?

@raymundomanzo8348 2 жыл бұрын

@@arthurlau2020 dont know if you still need this but what wiki says is how you find the root of an equation using newtons method while this video is how you find the error in every sequence of your solution using newtons method

@arthurlau2020 2 жыл бұрын

@@raymundomanzo8348 Although I already solved the problem, but still I appreciate your help and time!

@namename3130 2 жыл бұрын

I wouldnt reccomend learning maths from wikipedia.

@jinsoku1911 2 ай бұрын

Lol... he is writing backwards. That is awesome he learned that. I don't think i have seen the perspective from the other side of a "blackboard"

@enocklangat632 Жыл бұрын

I am confused by the method, I thought that method is for Newton's raphson not secant

@abdoulie1027 6 ай бұрын

🎉

@shashank_kishore_ 7 ай бұрын

❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤

@rahuljalgaonkar3808 2 жыл бұрын

Respected sir , Please answer my below question it's very imp for me!! Q. Newton's method converges faster if f'(x) is: A. 0 B. Large C. Small D. None of these

@namename3130 2 жыл бұрын

Is this an exam question? lol

@namename3130 2 жыл бұрын

If f'(x) is 0 at any point then it wont work, and f'(x) changes with every iteration so you need to be clearer. Do you mean f'(x) initially, or at the root or what?

@6Scarfy99 Жыл бұрын

large

@namename3130 Жыл бұрын

@@6Scarfy99 you would have to be making an assumption there

@user-eq6te1mw8e Жыл бұрын

@@namename3130 if f'(r) = 0 the method converges but linearly

@no-po9nv 2 жыл бұрын

You are not expanding around e_n = 0 at 2:41, sorry. You are expanding around r, f(r-en) = f(r) +(r-en-r)f'(r) + ... = f(r) - enf'(r). I get what you mean but the way you said it is probably why you have 2,000 views. You are technically correct but you skip so many steps in this video I don't even know why you bothered making it. I'm a mathematician and I do not know any engineering students who would understand this.

@ProfJeffreyChasnov 2 жыл бұрын

It's lecture 17 of a Coursera course that students should take after having taken Matrix Algebra, Differential Equations and Vector Calculus. But yes, this is one of the more difficult lectures for the students. A harder problem is finding the order of convergence for Secant's Method.

@sunegraversen6492 2 жыл бұрын

not trying to white knight but im a high school student and with reading up on some of the maths behind this I could follow these steps, and this video helped me a lot with an essay i'm writing.

@michaelmcleary8566 2 жыл бұрын

Well Mr Smart Arse mathematician, why don't you make a video and post it up. I've noticed there's absolutely nothing via your name link and as actions speak louder than words, you probably have very little to say, apart from wry criticism.

@evgenyk.9291 Жыл бұрын

Completely agree. I am also mathematician and it took me like 10min to understand all missed steps with misleading information.