Newton's Method | Lecture 14 | Numerical Methods for Engineers

Derivation of Newton's method for root finding.
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[@David-cx3fc]

This is an amazing explanation. I took a Numerical Analysis course a couple years ago where we used it, but this really helped me gain a much deeper understanding. Thanks!!

[@python1419]

Clear explanation and straight to point. Thank you!

[@blessingmutema2768]

Prof you explain this very clear thank you SIR😊

[@Arwa57ar]

such a nice explanation, thank you very much.

[@madhukavirajith2040]

Thank you very much!

[@joshuathemathsciencewizard4572]

Bravo !

[@stephenmurichu4559]

Thanks a lot

[@viva_la_nature]

Damn i'm actually learning

[@OjulongClement]

nice lesson thanks

[@willymuller970]

Thanks for your good explanation. I am a bit puzzled with the expression of f(x)=x^2-2. How did you get that? I am wondering what if another value apart from sqrt of 2 is to be found, then that means we should also guess another expression of f(x) right?

[@ProfJeffreyChasnov]

The square-root of 2 solves this equation.

[@Jefferson_Conza]

Well, you need "to solve" for √2 right? Now, Newton's Method works for functions with template f(x)=0. So, in this case you do: x=√2 x²=(√2)² x²=2 x² - 2 = 0 (our function) Finally: f(x) = x² - 2 (which is the function that works for sqrt(2)) If you speak Spanish (or if not, turn on captions), you can get another grasp in this video :) kzbin.info/www/bejne/pWGzkmuLr7RpaKs

[@yiwang3437]

Square root 2 is the answer to be found at y=0. The function X^2 +2 is only served as an example, other functions which has x=square root 2 at y =0 would do the same.

[@hitthemill8595]

x^2=2 => square root of x^2 = square root of 2, thus at the initial one instead of x^2=2, we just write x^2-2=0

[@jersolbobila8451]

We will satisfy f(x) =0 if we use the equation f(x) = x² - 2, i.e., f(√2) = (√2)² - 2 = 2 - 2 = 0

[@elaheataei7805]

Can you please explain the matter of selecting the right X0? such that if a sufficient x0 is not selected the assumption of (x-x0)^2 < |x-x0| is not true. How should I determine if a correct X0 is selected? I know the Burden book for Matlab coding gives an explanation of this by the Taylor polynomials series, yet it is not understandable.

[@0397luas]

You can choose any Xo. That's the point. So let Xo=sqrt(2), you can choose any number in between 0 and 2. It will have to be in between since 0

[@user-wi4vv5cm5o]

how can use matlab to deal with the differential without using syms for usual case?

[@ProfJeffreyChasnov]

I always differentiate by hand.

[@fireflylyrics3528]

isn't there something wrong? aren't we supposed to substract aff xn then subtract f(x)/f'(x) ?

[@natalijamarkovic3654]

Hello, this video was really helpful, but I have one follow-up question. How do we determine the last iteration for a general case, or what conditions do we need a solution to satisfy in order to consider it as the most accurate?

[@ProfJeffreyChasnov]

Test convergence by comparing the last two iterations.

[@baxterkakulas3743]

idk abt u guys but im droping 24/30 on this investigation

[@bryanw967]

pretty solid

[@alimishina5821]

Is this the same as Newton-Raphson method

[@ProfJeffreyChasnov]

Yes

[@erebiporbs9790]

Why did you use x0= 1

[@ProfJeffreyChasnov]

Could use a different value.

[@bonganimathebula3210]

If you let f(x)=x - sqrt(2) you'll get a more accurate answer quickly (After the 1st iteration)

[@ProfJeffreyChasnov]

The idea is you don't know what the sqrt(2) is!

[@chabotaluputa7665]

Thank you❤

[@chabotaluputa7665]

Tour amazing ❤

[@pieroc.3440]

Thank you very much!