Horner's Method

  Рет қаралды 88,144

Oscar Veliz

Oscar Veliz

Күн бұрын

Пікірлер: 37
@faisca468
@faisca468 6 жыл бұрын
Thank you so much! I finally understand this, thanks to you. The history part was interesting as well. Great video!
@victormartinezbernal9674
@victormartinezbernal9674 3 жыл бұрын
omg thank you so much, i dont know why there arent much theory vids and only "resolving excercices " vids i just wanted to understand why i was doing what i was doing and why it was right. Some wise person said once "theres not better practice than a good theory" .
@jihan6780
@jihan6780 4 жыл бұрын
Thank you so much. I couldn't have asked for a better explanation!
@Ahmadali-vd3ee
@Ahmadali-vd3ee 4 жыл бұрын
very well organized explanation.Thank you!
@EinstienJr
@EinstienJr 4 жыл бұрын
Thanks, great video. I'm here trying to solve horner's method using recursions (thought I had no interest in root-finding)
@hannaafesa
@hannaafesa Жыл бұрын
Great Work
@AJ-et3vf
@AJ-et3vf 2 жыл бұрын
Awesome video! Thank you!
@md.adnannabib2066
@md.adnannabib2066 3 жыл бұрын
Man you are the only one who have shown history.not only that you have mentioned what muslim mathematician did.In todays world our contribution in math and science are not heard.thanks man.I love how you show how mathematician all around the world invented same topic,without restricting only what europeans discovered.
@heeheehaha45
@heeheehaha45 2 жыл бұрын
Dear Oscar, may I know if there are methods for solving system of polynomials equations? (I have watched your series of Newton's method, however, even global Newton's method might stuck at some local minimum point, right?)
@OscarVeliz
@OscarVeliz 2 жыл бұрын
I haven't covered anything specifically for systems of polynomial equations. But for solving systems of nonlinear equations, the generalized secant method kzbin.info/www/bejne/pmOygZ-kfa-DhKs tends toward convergence. Also, Generalized Aitken-Steffensen Method guarantees convergence kzbin.info/www/bejne/Y6mckJmJg9eLadk
@heeheehaha45
@heeheehaha45 2 жыл бұрын
@@OscarVelizThankyou Oscar!
@dzertblue8015
@dzertblue8015 3 жыл бұрын
excellent teaching! respect...
@ayoubsbai6339
@ayoubsbai6339 3 жыл бұрын
You give me the 3Blue1Brown vibes haha, loving what you do anyways, keep it up~
@michatarnowski580
@michatarnowski580 5 ай бұрын
I would really like to see a proof of why Horner scheme gives the quotient. I understand why it gives the remainder of division, but it giving the quotient looks like magic. I saw some proofs by solving equations for polynomial coefficients, but I wonder if there's a quick and simple argument, at least for low degrees like 2 and 3.
@karenslivesmatter2186
@karenslivesmatter2186 2 жыл бұрын
I still don't get it why does when you multiply all the roots of the quotient it is equal to using synthetic division
@alexandrevachon541
@alexandrevachon541 4 жыл бұрын
For more efficiency, you could also replace the Newton step in the Newton-Horner method with the Halley step to create Halley-Horner, or with the Householder step to create Householder-Horner. But what if you wanted to avoid derivatives? Then switch to Steffensen's method to create Steffensen-Horner, or to the secant method to create Secant-Horner.
@OscarVeliz
@OscarVeliz 4 жыл бұрын
Or you switch to finding multiple roots at once such as with Bairstow's Method, Durand-Kerner Method (kzbin.info/www/bejne/a3vGoYKgZ7CnjcU), or Aberth-Ehrlich Method (kzbin.info/www/bejne/jnrddK2cgqmGsM0); all of which even find complex roots by default.
@alexandrevachon541
@alexandrevachon541 4 жыл бұрын
@@OscarVeliz By the way, you didn't showcase the secant fractal... but I have generated some fractals from it. So no need to showcase it?
@OscarVeliz
@OscarVeliz 4 жыл бұрын
I'm not quite sure what you mean.
@alexandrevachon541
@alexandrevachon541 4 жыл бұрын
@@OscarVeliz Yeah. It reminds me for Bairstow's method being explored in much detail, still waiting in the queue... The problem with these methods, is that my calculator doesn't support complex numbers, and I have to do it by hand.
@manassrivastava5901
@manassrivastava5901 2 жыл бұрын
Excellent
@jahjahjah213
@jahjahjah213 5 жыл бұрын
Is it just me or does he sound like 3blue1brown
@SaifUlIslam-db1nu
@SaifUlIslam-db1nu 4 жыл бұрын
I stopped halfway, then had to check the name as well.
@ayoubsbai6339
@ayoubsbai6339 3 жыл бұрын
I almost thought he is Grant tho
@halalos
@halalos 4 жыл бұрын
u are a god
@holyshit922
@holyshit922 2 жыл бұрын
What about version for quadratic divisor ? It would be helpful for deflation with quadratic with complex roots
@OscarVeliz
@OscarVeliz 2 жыл бұрын
Consider using Durand-Kerner (kzbin.info/www/bejne/a3vGoYKgZ7CnjcU), Aberth-Ehrlich (kzbin.info/www/bejne/jnrddK2cgqmGsM0), Laguerre's Method (kzbin.info/www/bejne/mJ2ycoWMadGhf68), or Bairstow's Method (in the video queue).
@holyshit922
@holyshit922 2 жыл бұрын
@@OscarVeliz speaking the polynomial root finding , there is also eigenvalue method There are two companion matrices in upper Hessenberg form and two with lower Hessenberg form and we can apply QR method to one of them, QR decomposition can be easily derived by multiplication by rotation matrices - from left to get R matrix and from right to get Q matrix How can I choose shift (without complex arithmetics) to accelerate the convergence There also slow convergence with repeated roots I wrote code for Bairstow's method based on one of the videos on youtube , I also wrote code for eigenvalues method but i probably didnt choose shift well and as stop condition i gave maximum number of iterations This approach is space costly but is implemented in Octave and numpy and even they dont manage the repeated roots
@Traymer7
@Traymer7 5 жыл бұрын
Hi, thank you so much for explaining, although I didn't get the Newton-Horners scheme - could somebody please tell me how did we get the new polynomials every restart of the method?
@OscarVeliz
@OscarVeliz 5 жыл бұрын
You use the quotient from Ruffin's Rule.
@amdomag
@amdomag 5 жыл бұрын
Nice video. Unfortunately, I find the derivative of your words with respect to time higher than average wpm though applying Rolle's Theorem this is not absolutely true. Just kidding. Please keep on posting videos.
@stingyfortnite3183
@stingyfortnite3183 6 жыл бұрын
Nice tutorial, next time explain history at the end for people who care, Thank you so much for this video though!
@marvel438
@marvel438 5 жыл бұрын
You can simply forward the video. Don't Be Stingy.
@nahiyanalamgir7614
@nahiyanalamgir7614 4 жыл бұрын
I usually skip parts of the video till I get something I want, often skipping by 5 seconds or fast-forwarding.
@sasirekhamsvl9504
@sasirekhamsvl9504 4 жыл бұрын
So we add use horner method to use newton method???
@OscarVeliz
@OscarVeliz 4 жыл бұрын
It depends. If you already have programmed a working Newton's Method, then you could use it as-is to find a single root (but it will be slightly inefficient). In order to deflate though you would have to apply Ruffini's Rule. But if you didn't want to use Horner's method, then you would need to divide your function call by the root you found, i.e. let newf(x) = f(x)/(x-r), as well as every other subsequent root that you find. For an example of using Newton-Horner, check out my implementation hosted in the channel's GitHub repository. The link is in the description.
@sasirekhamsvl9504
@sasirekhamsvl9504 4 жыл бұрын
@@OscarVeliz Thanks
Durand-Kerner Method
8:44
Oscar Veliz
Рет қаралды 4,3 М.
MAGIC TIME ​⁠@Whoispelagheya
00:28
MasomkaMagic
Рет қаралды 22 МЛН
Who’s the Real Dad Doll Squid? Can You Guess in 60 Seconds? | Roblox 3D
00:34
黑的奸计得逞 #古风
00:24
Black and white double fury
Рет қаралды 29 МЛН
Ouch.. 🤕⚽️
00:25
Celine Dept
Рет қаралды 29 МЛН
How Math Becomes Difficult
39:19
MAKiT
Рет қаралды 183 М.
The TRIPLE FOLDING phone has a Problem.
12:54
Mrwhosetheboss
Рет қаралды 2,3 МЛН
Solving Higher-Degree Polynomials by Synthetic Division and the Rational Roots Test
9:22
"A Random Variable is NOT Random and NOT a Variable"
29:04
Dr Mihai Nica
Рет қаралды 42 М.
Russell's Paradox - a simple explanation of a profound problem
28:28
Jeffrey Kaplan
Рет қаралды 8 МЛН
Introductory Calculus: Oxford Mathematics 1st Year Student Lecture
58:03
Oxford Mathematics
Рет қаралды 10 МЛН
Some silly number systems
8:17
Random Andgit
Рет қаралды 150 М.
MAGIC TIME ​⁠@Whoispelagheya
00:28
MasomkaMagic
Рет қаралды 22 МЛН