Secant Method

[@WaitinForAMate]

Quick, efficient and explained thoroughly with clarity. Educational videos like yours are the best, cheers

[@Q_z_]

9 years later... still helping some helpless student like me out and not wasting ay necessary time to explain. Thanks so much!

[@johannaw2031]

What a relief. I didnt even have to focus. You just gave me the knowledge. This is how teaching is supposed to work. Thank you!

[@AdityaFingerstyle]

Your video, although shorter than most videos on KZbin, is by far the best one. Short and clear - that's how I like my tutorials

[@kolcha]

Oscar, you are one of the best teacher I have ever seen. You gave extra critical information that make grasp of the concept easy and pleasant. Cheers from the Great Khurasan, Land of Al-Khawarazmi

[@dmitrijskass6760]

Clearly shown, clearly explained, clearly compared with other methods. The 3rd part is what is almost always missing in the other tutorials. This tutorial is just perfect. Thanks!

[@anastasiagavrilita6567]

Half of a semester was outran by your explanations (even those at the end of the video, where you explain why we should know all 3 methods). Sir, thank you!

[@-i3ird-p156]

This saved me so much times, while giving me enough explanation to help me understand it. Thanks for the video, you are the best.

[@CristianGhervasa]

11 years later, still efficient! thanks a lot, i finally understand the logic, in the teacher's book it's kind of unexplained

[@omkardhami2687]

Very clear, enjoyed all your videos. You taught me in 4min what I spent 30min trying to figure out from lecture notes. Thanks!

[@theyammi437]

Simply put and straight to the point. If only Textbooks were this way.

[@mopeppermomoney]

If only my textbook would say things this clearly. Thank you!

[@jotieshagi5954]

Hands doen best tutorials on numerical analysis on youtube. keep on rockin man

[@timmy3211]

It says a lot about your dedication that your 10 year old video had the newish feature of chapters added to it, nice job.

[@jackieduy4008]

DOES NOT GET BETTER THAN THIS. 45 min lecture compressed into 3 min!!!

[@nikolajlapkovskij]

Absolutely fantastic explanation. Even after 12 years. Huge thank you and much much much appreciated!!!

[@wolfix20021]

Thank you so much! just within 4 minutes you open gates of the secant method. Much appreciated!

[@AJ-et3vf]

Awesome. Nice and concise with clear visuals and lucid explanations.

[@SumitYadav-mx8bp]

Clear, meaningful and thoroughly explained..this the kind of video which makes learning so simple and enjoyable.. nowdays... thanks for uploading :)

[@ghelbymuhammadfaid9329]

Sir, you saved my life. Thank you very much

[@loverhajverian]

excelent dude :) i missed the class , but u helped me in covering the missed lecture. GOOD JOb

[@AbhishekKumar-vf5ep]

Thanks for explaining in simpler way...😊

[@tauseefrehman7909]

Thanks so much man, that video was very concise and to the point!

[@kingKabali]

Superb!! Why I didn't find at the start of the semester.

[@moizhd9132]

Thanks mate! You saved me from failing a maths test

[@littleflower782]

Has my semester been actually saved in 4 minutes?????

[@squareroot1698]

I reckon! Bloody good insight. Clear, concise and articulately making sense of all three methods. Fire stuff

[@WJ-gs8kk]

very clear and easy to understand! Thank you!

[@zeynepbetulkaya3645]

So clear, thank you

[@heromiIes]

Great job. Keep making good videos like this.

[@RebeliousSapien]

Thank you. This was extremely helpful.

[@ChuckRage]

This was very helpful, thank you.

[@pekou785]

Well presented!Keep it up!

[@rajangupta732]

It was truly Awesome

[@micelamicela]

Thank you! Very clear.

[@gecaprathamesh6583]

Nice video! Concept clear!!!Thanks :)

[@michaelprovost6066]

Thank you! This is excellent!

[@ronanm4418]

BRILLIANT!

[@PiyushGuptaknl]

you are the saviour dude!!! :D

[@raen714]

Thank you for this video! I could not find an understandable explanation for this method anywhere in the textbook and my professor has been travelling a lot lately, so jet lag made him mildly incoherent.

[@lucianoinso]

Clear and to the point (root? lol), thank you!

[@jacquesbautista-plante5497]

my teacher explained it terribly, thank you so much for clearing up this muck!

[@dakshadaksha1071]

Thanks for wonderful lecture

[@HellOnGames]

Thanks! You saved my day.

[@emiliskakanis9911]

best example i saw throw all youtube

[@hossiluc]

Thanks for your service

[@aenesturan]

great video, thank you

[@martinz6445]

Oscar, you are a legend, thanks

[@StarryGlobe089]

perfect explanation!

[@GIChiyo]

Thank you so much, your videos are fantastic!

[@9Patroclus]

Thank you, mate!

[@SempatikBalkc]

so succesfull thank you

[@daliaruizdiaz2024]

fuck, i was looking for your channel all this time and NOW I find you, ONE DAY BEFORE MY EXAM. Anyway, Thanks for the explanation :) prepare yourself for spam :) I'm gonna watch your entire channel in one night

[@rankintoday]

Great Video. Thank You. Saved me lots of time.

[@scilabo]

great explanation. clear.

[@ugottabefresh]

THANK YOU

[@DanielViolet1]

YES! thank you :')

[@15october91]

THANK YOU!

[@15october91]

Over two years later I still think this is a great video!

[@manasisrivastava3313]

Thank you so much! :)

[@EbraM96]

Way to go.

[@shlomohadar3194]

bless you.

[@dansxie9340]

thanks all for the all nonlinear equation method!!!!

[@srikrishnamaths788]

👌🙏

[@ramananramaswamy2763]

If possible upload a beautiful video regarding regula falsi

[@OscarVeliz]

My pleasure kzbin.info/www/bejne/ppiUemt3fJpsf80

[@joannasalazar7095]

thanks

[@palmoasis]

one question, why did we stop when the value of Ea was 9.6% and not when it was 60.something %?

[@frisynovel2374]

This video aged well like a Fine Wine!

[@prantikdas6218]

What books do you read for numerical analysis?

[@OscarVeliz]

In my more recent videos, I try to use and show original papers, especially when a method is named for someone. Otherwise, the most commonly used books I've used on this channel have been "Numerical Methods That (Usually) Work" by Forman S. Acton, "Elements of Numerical Analysis" by Peter Henrici, and "Numerical Recipies" by Press et al.

[@sahandanushka7371]

Should we pick X1 and X2 like [f(X1)0] or [f(X1)>0 and f(X2)

[@OscarVeliz]

Picking points where the function has different signs is a good strategy which is also used by Brent-Dekker. Another is to pick two points that are very close together to better approximate f'.

[@sahandanushka7371]

@@OscarVeliz Thanks 🤩🤩 this video really helped me

[@vangelis_tr6132]

hello!!! Thanks for the explanation. I just have one question. What is the M?

[@OscarVeliz]

Check out my video on order of convergence kzbin.info/www/bejne/gIXMn5imedNkmqs

[@OscarVeliz]

@raen714 You're very welcome.

[@faheemrajuu]

when you will understand the whole thing... you would be like "excellent!!!"

[@omkarrr24._92]

The x3 you took i.e x3= 3 … (2:19) In the above line you have mentioned that x n+1 So if you are taking xn as x2 then only it satisfies the formula . Maybe it's wrong . Or I'm not able to get it !!

[@OscarVeliz]

I'm not sure I understand the question. With the current iteration (in this case n=2) the next iteration count is n+1 (here 3). This means to find x_3 we'll need to use the previous two x values saved inside of x_2 and x_1. Those were the numbers 3 and 2 to start with. Then replace everywhere we have x_2 with the number 3, and x_1 gets replaced with the number 2. The result 2.423.... gets stored into x_3 and then we repeat using the latest two numbers x_3 and x_2 to compute x_4. And so on.

[@omkarrr24._92]

@@OscarVeliz ok got it , thnx ♥️

[@gaaraofddarkness]

2:45 how did you arrive at the expression of alpha as the ratio of error ratios?

[@OscarVeliz]

Check out my video on order of convergence kzbin.info/www/bejne/gIXMn5imedNkmqs

[@Peter-bg1ku]

Great video. Open a Patreon page perhaps. You deserve a coffee.

[@OscarVeliz]

I have a GitHub Sponsors page on the code repository for the channel github.com/sponsors/osveliz if you'd like to support what I do.

[@karteektavarageri5140]

for doing secant method, do we also need take into account the change in signs to determine what our next values become?

[@OscarVeliz]

Short Answer: Secant Method doesn't consider signs. It just uses the iteration function. Long Answer: Using where the function changes sign is a good strategy for picking starting points. If you force Secant Method to always consider signs, then you are essentially using Dekker's Method (kzbin.info/www/bejne/Y5OvhIWfpNCafM0) which guarantees convergence to a root.

[@karteektavarageri5140]

@@OscarVeliz Got it, thank you so much Oscar, much appreciated.

[@OscarVeliz]

On second thought, forcing Secant Method to always have different signs would actually be more in line with False Position Method kzbin.info/www/bejne/ppiUemt3fJpsf80

[@karteektavarageri5140]

@@OscarVeliz Ahh ok, yea I see the resemblance. I don't really know the other method, but I do know false position. Thanks Oscar.

[@JayRD98]

So you pick x1 and x2 random?

[@OscarVeliz]

Try graphing. Picking two points where the function has opposite signs is also a good strategy like you do with Bisection (kzbin.info/www/bejne/g52zkIpjpMeohMk), False Position Method (kzbin.info/www/bejne/ppiUemt3fJpsf80), or Brent's Method (kzbin.info/www/bejne/Y5OvhIWfpNCafM0).

[@ilyaanufriev1344]

It's funny that you say about danger of devision by zero as if you die if you do it.

[@kikokimo2]

How to test if this method converges? Is there a way like for Fixpoint iteartion, to try g'(x) < 1?

[@OscarVeliz]

Secant Method is an "open" method like Newton's and doesn't have a convergence guarantee. There is a way to force Secant Method to converge which is the basis for the Brent-Dekker Method which I have a video on kzbin.info/www/bejne/Y5OvhIWfpNCafM0

[@EbraM96]

But how can I efficiently choose the first two points ? or should I just randomize them ?!

[@OscarVeliz]

The points you pick should vary depending on your function and how you know it behaves. Completely random and far away points are probably not efficient. I'd recommend either: picking two points that are close together (giving you a close approximation of the tangent) or one point where you know your function is positive and one when your function is negative (so that the secant might intersect the x-axis near a root).

[@jamiemedalla6326]

sir where did you made your graph presentation

[@OscarVeliz]

A free program called Microsoft Mathematics. The new version is called Microsoft Math Solver.

[@naradaabeysekara]

How to pick X1 and X2 values?

[@OscarVeliz]

Try graphing. Picking two points where the function has opposite signs is also a good strategy like you do with Bisection (kzbin.info/www/bejne/g52zkIpjpMeohMk), False Position Method (kzbin.info/www/bejne/ppiUemt3fJpsf80), or Brent's Method (kzbin.info/www/bejne/Y5OvhIWfpNCafM0).

[@lounesbenali4889]

3:50 No, you Thinks !

[@AlexanderHL1919]

But my dude, this is not the Secant method... You showed the False Position Method which is a Bisecant-Secant hybrid method.. Will the real Secant Method please stand up?

[@OscarVeliz]

I have made a video on False Position Method kzbin.info/www/bejne/ppiUemt3fJpsf80 The usual form of Secant Method is x_n = x_(n-1) - f(x_(n-1) * ((x_(n-1) - x_(n-2))/(f(x_(n-1)) - f(x_(n-2))) but by multiplying both the nominator and denominator of the fraction by 1/(x_(n-1)-(x_(n-2)) you get form I show which looks a lot like Newton's Method without the derivative. I also prefer to use n+1, n, and n-1 instead of n, n-1, and n-2.