False Position Method - Regula Falsi

[@adityasher]

Dear Oscar, I was searching for a good video, the other videos had large number of views but they sucked, you were to the point, professional and correct. This suggests you are not here for money but for teaching. Loved this video.

[@veznan4305]

5 years later and still super helpful!

[@Dicergrey]

You elucidate the method effortlessly in such simple words. This channel is pretty helpful in helping me, a beginner easily grasp the steps of these methods, found it jus now.

[@wolfix20021]

Short yet quite adequate, Thanks a lot!!!!

[@Emile50]

This isn't only in reference to this vid, but to your vids in general: Your explanations are truly great, they're coherent, concise and easily digestible.

[@jackieduy4008]

Dear Oscar, you are straight to the point and so easy to understand. On behalf of all the 47k view, thank you!!!

[@chamathdayanudugampola6950]

honestly, a gift from god

[@martinfiedler4317]

Wow. Best explanation I found so far. Thanks!

[@manojmani2061]

Its Mind Blowing ... Gone through KZbin more dhan 30 minutes. Havnt found a good video with a great explanation like yours. Its so simple to understand... Keep on teaching 👍👍👍

[@marcuskrahenbuhl1009]

Just found your videos today, fantastic way to visualise how these processes work - thank you for the time and effort you have put it

[@TheBenjaminVrenko]

Hey man just want to thank you for your videos, you've helped me immensely with my numerical mathematics exam, one of the most useful and helpful channels on KZbin, you explain stuff in a matter of minutes and I can immediately understand everything!

[@ilde4]

Absolutely fantastic video. So easy to follow with excellent graphics.

[@pandora7372]

I think I found the right video after searching for a long time. Thanks for sharing.

[@kurtzedrickbaldemoro9178]

This is a great video! Math, more than anything else makes more sense when visualized, thanks this is helpful :)

[@AJ-et3vf]

Nice! I finally understood this method. Great concise video.

[@therealmisteroofoof4001]

You are absolutely amazing and these videos are gold. Thank you so much!

[@THAdeeHARMONY]

You’re a great teacher

[@Icaruskid]

Thanks so much! Helped me a ton on my homework assignment. Off to Newton-Rhaphson!

[@nikirangdan__]

"Imagine if bisection method and secant method had a child, they would call it false position method" LMFAO IM FUCKING ROLLING ON THE FLOOR

[@marthabustamante566]

Thank you Mr Veliz. Very clearly explained.

[@nikhileshthakur894]

Really liked your video. I would request if you would put few more videos related to power method , greshgorin circle theorem and few of the numerical analysis on differential equations. This would be very much helpful.

[@abcd1234-rambo]

Sir more videos are needed । I am from Bangladesh

[@phy_dude]

Underrated

[@Nailartco]

I LOVE YOU. Thank you!!!!!!!!

[@matlabtraning7675]

Hi Oscar! Wonderful video, and thanks for your effort! I'm wondering if you are familiar with a variation of the Regula Falsi method, proposed by C.J.F. Ridders in his article "A new algorithm for Computing a Single Root of a ReaL Continuous Function" (IEEE Transactions on Circuits and Systems, vol. CAS-26, No11, November 1979, pages 979-980). In "Numerical Recipes in C", second edition, the authors claim that the method has a quadratic order of convergence, which will be quite an impressive improvement if we consider the jump from linearity to factor 2. I tried to understand more deeply what exactly this method does and if is true that the order of conversion is quadratic, but unfortunately not with big success. I think that your videos about root finding aren't complete without this method and I will be very grateful and happy if you will find some time to invest in creating a new one that will treat this method. Thanks in advance and keep doing what are you doing, you're the best!

[@jyukari5201]

Thank you so much! The video is really helpful.

[@srikrishnamaths788]

Nice Information Sir 👌

[@rudnam]

Thank you so much

[@marthabustamante566]

Great Video!

[@boggavarapunikhil2745]

Nice

[@n1rvanalight]

Great video oscar :)

[@AxiePlays601]

Thanks

[@warrencoons3184]

Appreciate the help

[@Foamboard-Flyby]

I have a question! Is it only possible to find one root at a time for functions with multiple roots? (eg quadratic functions) I created code that performs Regula Falsi and it can only find one root but I’m wondering if it’s possible to find the others.

[@OscarVeliz]

It converges to one root at a time, but you can restart with different intervals to find the other roots of your function.

[@bigmom9303]

Thank you!

[@javigg4624]

Thank you soo much

[@emirbfitness]

goat

[@habibullahamjad2037]

I want to a video of how regula falsi is mathematically same like regula falsi can be converted to secant method so they are mathematically same you why we call a secant method a contribution how these two are different

[@sebastianeriksson7949]

Great, we are currently calculating the rate of convergence for each root in a functiion. Do you have any tips to do this numericaly on the computer?

[@OscarVeliz]

I have examples of computing rate and order in this video kzbin.info/www/bejne/gIXMn5imedNkmqs and as far as a tip, I'd recommend trying different starting intervals if you are using regula falsi.

[@razvanchiose6523]

thanks

[@inperpetuum4211]

0:41 what to do if f(a) and f(b) have the same signs?

[@OscarVeliz]

You could try iterating anyway in the hopes that it eventually finds an interval with different signs, but a key assumption of Bisection and False Position has been broken so there wouldn't be any guarantee of a solution.

[@subhashsarangi]

Can you explain the difference between secant method and regula falsi method.

[@OscarVeliz]

Have you seen my video on Secant Method? kzbin.info/www/bejne/lX7Jm4uFgbqhr9k

[@presidentevil9951]

I was solving for x^5+5*x-1=0 i was using bisection/midpoint and false position/root methods. i used lower limit 0 and upper limit 10 for both. The bisection/midpoint method converged in less than a second. I needed only few iterations The false position/root method I ran for more than a day and it still didn't converge. Even after several iterations it was converging extremely slowly. The false position is faster????

[@OscarVeliz]

It is a good idea to add an iteration cap (something like 100 iterations) just to make sure your code doesn't run forever. You are also using an interval with large values for your function (10^5 + 5*10 + 1 = 100051) which is not ideal. If you used an interval like [0,1] where the function evaluates to 0^5+5*0-1 = -1 and 1^5+5*1-1 = 5 then you'll see false position running much faster than bisection (about 10 iterations to 24 iterations).

[@presidentevil9951]

@@OscarVeliz I tried 0 to 1 with the false position/root method and it was very fast. i tried 0 to 2 and it is still taking forever. i did 0 to 1000000000 for bisection/midpoint method for the equation and it still completed very fast but 0 to 2 for false postion/root method takes forever? I still question whether midpoint or root method runs faster?

[@OscarVeliz]

@@presidentevil9951 as I mentioned at 3:05 both methods have a linear order with the M value for Bisection always being 1/2 but the value for False Potion is dependent on the function. I also mention at 3:28 that False Position can be just as slow as Bisection (you've identified an interval for which it is slower) but that it is usually faster.

[@presidentevil9951]

@@OscarVeliz I wished it was mentioned in your video that False position can be slower than bisection instead of "just as slow" "you've identified an interval for which it is slower", in this case significantly slower. In fact I sent the previous message about 0 and 2 interval and even NOW it is STILL running. I'm starting to question why use false position now since bisection is more reliable? Is it possible to show me an example of which bisection/midpoint method takes forever and false position/root method is quick? (Since what you showed me that False position/Root method is only slightly faster than bisection/midpoint and since computers are very quick I can barely notice the difference)?

[@OscarVeliz]

@@presidentevil9951 Recall again that for the interval [0,1] False Position was indeed faster than Bisection (less than half the iterations). Again, adding an iteration limit (say 100) will prevent your code from running for forever. Bisection guarantees a value of 1/2 for M no matter the function, meanwhile False Position does not have such a guarantee. I also mentioned at 3:28 that there are ways to improve the performance of False Position method (these improvements can also increase reliability). If folks want, I can make a video covering these in the future.

[@nimrakhalid7211]

why we call this method as false position method??plz reply

[@OscarVeliz]

Historical approaches used a name similar to "two errors", which later was translated to a Latin/Italian vernacular by Fibonacci, and others, coming to be known as "false positions" and then Latinized again to regula falsi. en.wikipedia.org/wiki/Regula_falsi#History

[@holyshit922]

They switch to the methods which do not guarantee convergence , strange approach

[@zombie-blood-490gaming5]

i love you

[@bansishah2091]

can you teach Matlab codes for these methods ?

[@OscarVeliz]

I do have code for these methods on GitHub github.com/osveliz/numerical-veliz some of which are in Matlab.

[@firmeljaravata7181]

NumSol brought me here haha

[@NINO.O403]

:*

[@EmbersNaiz]

you sound oddly a lot like 3blue1brown :v

[@OscarVeliz]

I started making videos way before he did (I went on a long hiatus during grad school) so technically he sounds like me ;) I actively try not to watch other math-tubers so that I can keep my videos original.