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!!
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?
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 :) ruclips.net/video/o0Pa8UzO62I/видео.html
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.
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?
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.
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!!
Clear explanation and straight to point. Thank you!
one of he best explanations out there
Excellent video sir💯
Is this the same as the Newton Raphson Iterativ System? Thanks
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?
The square-root of 2 solves this equation.
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 :)
ruclips.net/video/o0Pa8UzO62I/видео.html
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.
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
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
0:58 why function have no squaring in it?
Damn i'm actually learning
Prof you explain this very clear thank you SIR😊
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?
Test convergence by comparing the last two iterations.
such a nice explanation, thank you very much.
Why the root is intersection with x axis? I thought it graph of a function where x getting squared, so root depends on x value
or y getting squared
isn't there something wrong? aren't we supposed to substract aff xn then subtract f(x)/f'(x) ?
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.
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
Very good video
Thank you very much!
how can use matlab to deal with the differential without using syms for usual case?
I always differentiate by hand.
idk abt u guys but im droping 24/30 on this investigation
pretty solid
Is this the same as Newton-Raphson method
Yes
why does he look like skinny Mike Ehrmantraut from Breaking bad.
😂
Tour amazing ❤
Thank you❤
nice lesson
thanks
Thanks a lot
Bravo !
Why did you use x0= 1
Could use a different value.
Mike? Is that you?
If you let f(x)=x - sqrt(2) you'll get a more accurate answer quickly (After the 1st iteration)
The idea is you don't know what the sqrt(2) is!
Thank you very much!