Newton's Method

[@vineetkumaranand1011]

In 2020 still this video explains the stuff so easily that no other video explains 🙏🙏

[@sinewavey]

Honestly, this video still holds up well after 7 years. Your stuff really helps, thanks!

[@basketvector7311]

Holds up well after 7 years. That's funny. This math is from ancient Greece isn't it?

[@sinewavey]

@@basketvector7311 Doubtful about Newton's method, but I think it's kinda clear I was referring to the video.

[@belu-film6335]

13 years

[@harjitsingh7308]

2019 and this video is still the best. Mathematics never changes, this video will still be as helpful in 100 years from now just as it is today.

[@oussamaelbazzim3578]

Its 2024 and this is still one banger of a video.Great explanation as usual.Many thanks !

[@mikepowell8291]

These videos are super helpful, an hour lecture condensed into 5 minutes!

[@luqmansen]

Wow, just found this gem in 2019, very simple explanation, great video !

[@ai_serf]

Wanted to learn about taylor series, the rabbit hole has taken me to this foundational level. I love how you suggest foundational videos! this is a key element in presenting material! Thank you for great idea!

[@panthopothik6338]

This is exactly what I was looking for. Thanks so much

[@conformist]

Very helpful video, simple and short, while still getting to the important points. Many thanks.

[@maddy112211]

Love your videos, they are so helpful in such a short amount of time. The only thing I would like to see is smaller subtitles!

[@OscarVeliz]

You can customize the subtitles how you like support.google.com/youtube/answer/100078

[@sushankhyachapagain788]

Great job dude. Your videos helps a lot.

[@aftabhassan8996]

@Oscar Veliz, great video! At 2:28 , isn't is x_n+1 = 1/2(x_n + a/x_n) though? Isn't it a + sign as opposed to a - sign?

[@OscarVeliz]

Yes it should be addition instead of subtraction. I don't know how I didn't catch that earlier. Thank you.

[@adelmalik9838]

good job and thank you so much very helpful

[@alexandrevachon541]

For x^7 - 1000, it means finding the 7th root of 1000. Speaking of square roots, have you heard of the fast inverse square root? This algorithm was used in the Quake III video game. With this algorithm, it resulted in a speedup of performance in the game, a very smart use of such a root-finding algorithm.

[@OscarVeliz]

I have heard of it but am not familiar with it. Might be worth looking into.

[@bradleyh614]

Thank you kind sir

[@mynoveladventures5425]

Thank you!

[@mjbaay]

Thanks!

[@chancewatkins5071]

Very nice demonstration, thanks for sharing; Jesus Christ Bless you! :)

[@yoyaya007]

waw bro thanks good job !

[@AJ-et3vf]

Love this!!! ❤️❤️❤️❤️

[@madawacko258]

Thank you

[@Maxim9575]

Could you explain the next thing? Maybe you know bezier curves and you know what in the most solutions use Newton-Raphson method. But as far we know we use this formula on every iteration t = t - (bezierX(t) - x) / derivativeX. But in here I dont understand why we are dividing bezierX - x on derivativeX. Why don't we simply divide bezierX on derivativeX. What is it "-x" and why does it require. P.S of course "x" is initial point on x axis.

[@koreedeiqbal9141]

Please explain Which software is used for this video making ❤

[@OscarVeliz]

PowerPoint and Microsoft Mathematics 😁

[@ccuuttww]

I think Newton's method can also find minimum or maximum value but I don't if it can handle the equation like this: (1+x*-2)^2+(1+x*-2)^2-0.001(1/(1-(1+x*-2)-(1+x*-2))) It is a discontinous function I have tried it with quadratic interpolation I get only the smallest local minimum

[@OscarVeliz]

You don't necessarily need to do interpolation. Like I mentioned in my video on Finite Difference Method (kzbin.info/www/bejne/sKfVhZyojLKteJo), when finding extrema, instead of where f is zero you find where f' is zero (just substitute f' for f). Take a look at my video on Newton-Bisection Hybrid (kzbin.info/www/bejne/fHWWc4OKgqx9mtU) if you want to keep Newton's Method within a certain interval.

[@tanjil3595]

Great

[@djamelaitamrane9226]

combining Newt and bisection gives more safety. i am looking for a C code with an example if it's possible .

[@OscarVeliz]

I have a video on Newton-Bisection Hybrid kzbin.info/www/bejne/fHWWc4OKgqx9mtU which includes accompanying code although not in C. One of the books I reference in the video does give C code.

[@tac6276]

So whenever we find the tangent line to the point X, the next X should be at the point where the tangent intersects the x-axis?

[@OscarVeliz]

Yes and I have code that will plot this for you on GitHub.

[@komaang3166]

i like all your videos.. how many videos in total have you posted please?

[@OscarVeliz]

I have posted 7 videos. You can find them all on this playlist kzbin.info/www/bejne/g52zkIpjpMeohMk

[@komaang3166]

Great I've viewed all of them. Very very helpful!! Can you do one also for Muller's method if you have some time..?

[@OscarVeliz]

I am glad these videos helped you. I do plan on making more videos, I'll add Muller's method to the list, however my priority at the moment is completing my dissertation. A quick note on Muller's. Recall that Secant method uses 2 points to create a line that crosses the x-axis. Where it crossed was your next x point. Similarly Muller's uses 3 points to create a curve, specifically a parabola, that usually crosses the x-axis at 2 spots. From those two points your new x will be the one where your function at that point is closest to zero. You'll then use that new x point, plus the last two of the three curve points, to make your new curve until you find the root.

[@komaang3166]

Alright ill try that out. Your help is much appreciated. All the best in your dissertation.

[@OscarVeliz]

I made a video on Muller's Method. Hopefully you'll still find it useful three months after asking for it kzbin.info/www/bejne/jnqsdp2tqdCChMU

[@بیرکاریفێربە-ك2ت]

Please,how do fined xo???

[@OscarVeliz]

The technical answer is to pick a value in the neighborhood of your root. Of course this would mean knowing the neighborhood of your root. You can always try graphing to find a close guess. Alternatively you could widen the interval of convergence which I have a video on kzbin.info/www/bejne/sKq7g6Juhs-dZqM which will allow a larger domain of starting values.

[@kikokimo2]

And what about the convergence? Is there something like g'(x) < 1? And how to calculate, after how many iterations it converges for a specific function? Like the bisection method?

[@OscarVeliz]

Newton's Method is considered "open" unlike Bisection, False Position, or Brent's Method which are "closed" inside an interval. It doesn't have a guarantee of convergence unless you find the interval of convergence which I have a video on kzbin.info/www/bejne/sKq7g6Juhs-dZqM

[@kikokimo2]

Oscar Veliz Wow! Never thought of an answer so fast, as the video is old! Thank you so much for replying! Gonna check it out tomorrow when I wake up and let you know my thoughts.

[@OscarVeliz]

I do my best to respond to comments. I've been trying to respond to one you left earlier on Fixed Point but KZbin isn't showing it to me. I look forward to your thoughts on the video.

[@kikokimo2]

And you're serving your "customers" so good I find! Thanks a lot for that! The question was about, how to come that root of "1.618" to test with it g'(x) (convergence test)! How to guess that, if we are actually "searching" for that root, and trying to see if the Fixpoint iteration converges? PS: The answer in the FAQ didn't help unfortunately.

[@OscarVeliz]

Note that it isn't g'(x) test but g'(r) test so it is better to think about it as "will this function converge to this root?" and even then, I wrote an example of a function failing the test but still converging so the test isn't so black and white. All it says is that if g'(r)

[@munydoggy]

how do you pick x1 sir?

[@Crossfire9211]

I believe you enter the value in the provided function, and see if the solution is close to the root ( close to F(x) = 0 ) It is an initial approximation

[@munydoggy]

Thank you so