Chapter 03.05: Lesson: Secant Method Example

Learn via example the secant method of solving a nonlinear equation. For more videos and resources on this topic, please visit nm.mathforcolle...

[@siddhantraj5323]

U can't take 4 and 5.5 because I believe for a root to exist, there must be 1 f(-) and f(+) value but f(4.5) and f(5.5) both are positive

[@numericalmethodsguy]

You are confusing secant method and false position method. The false position method (mathforcollege.com/nm/topics/false_position.html , a bracketing method, uses secant lines to estimate the root of an equation. The secant method (nm.mathforcollege.com/topics/secant_method.html , an open method (estimates do not need to bracket the root), uses secant lines to estimate the root of an equation.

[@RobertoEmilioRomero]

Siddi RJ he just did and it worked. Do u have a counterexample?

[@RobertoEmilioRomero]

Siddi RJ ur talking about bisection method.

[@vijayshankar9529]

both the links are dead...@@numericalmethodsguy

[@numericalmethodsguy]

@@vijayshankar9529 Please send me the links through this comments section.

[@silverplasticware]

Wow, this was incredibly clear and concise. My professor does not bother giving any examples, so this was very helpful. Thank you very much!

[@numericalmethodsguy]

The secant method is derivable from Newton Raphson method by approximating f '(x(i)) by a backward divided difference approximation. That approximation is the slope of the secant line between points [x(i),f(x(i))] and [x(i-1),f(x(i-1))]. If you doubt that it is secant method, what is it then!

[@himildesai9898]

thanks dude...you saved my life...awesome video...I now understand Secant method so perfectly.

[@SameeKhanSamee]

Alhamdulillah, i understood clearly. May Allah bless you

[@bharadwajpawar9374]

inshallah

[@bharadwajpawar9374]

khuda fiz

[@biggbuggy]

Mr numericalmethodsguy you are awesome!! Go go professor!!

[@sunz.6072]

Thankyou so much for explaining everything so clearly and so thoroughly without skipping any steps. You videos are so beneficial for me and I recommend them to all my friends. You sir, are an amazing teacher.

[@numericalmethodsguy]

Thank you. To get even more help, subscribe to the numericalmethodsguy channel, and go to MathForCollege.com/nm and MathForCollege.com/ma for more resources and share the link with your friends through social media and email. Support the site by buying the textbooks at www.lulu.com/shop/search.ep?keyWords=autar+kaw&type= Follow my numerical methods blog at AutarKaw.org. You can also take a free online course at www.canvas.net/?query=numerical%20methods

[@JeetKuneDofive]

You are amazing you are helping me pass my class.

[@numericalmethodsguy]

No, it is not the same. The secant method and regula falsi use the same formula for finding the next estimate of the root, but here is the scoop. The secant method is an open method and hence does not require the two previous estimates to bracket the root; the regula falsi method is a bracketing method and the two previous estimates have to bracket the root in every iteration.

[@numericalmethodsguy]

It is the same as (a-b) divided by (c-d) is same as (b-a) divided by  (d-c)

[@Benerbz8]

Your formula has a mistake in it! My textbook reads: x(i+1) = xi - f(xi)(xi-1 - xi) divided by f(xi-1) - f(xi)

[@RobertoEmilioRomero]

Benerbz8 theres is no mistake. Rearranging the (xi-xi-1) into (xi-1-xi) in the numerator introduces a negative sign. Rearranging f(xi)-f(xi-1) in the denominator into f(xi-1)-f(xi) introduces another negative sign. Both negative signs in numerator and denominator both divide out to + since -÷-=+ . He just has the equation arranged algebraically different but mathematically and graphically identically equal. Simple algebra. Remember (xi-xi-1) = -(xi-1-xi) and f(xi)-f(xi-1) = - [f(xi-1)-f(xi)] . The negative signs introduced in both rearrangements dividie and cancel out to +1. I hope you saw it man. Best. Simple algebra.

[@RobertoEmilioRomero]

There is no mistake in his formula. Im guessing you guys who agree he has a mistake in his formula are not very good in catching algebra mistakes or are intermediate level. Any advanced level student would see his equation is the same as the otherguys multiplied by 1.

[@RobertoEmilioRomero]

Ur comment was 5 years ago. I hope if u see it now you realized your equation and his are one and the same.

[@erkansenol9891]

Thanks from TURKEY

[@KpopOrigami]

Yay! now i can do my presentation on the Secant method!! thank you so much!

[@numericalmethodsguy]

I do not have access to the studio this semester.

[@unknownkingdom]

These are very useful videos. Thank you for posting.

[@elsbbbb1]

you explained everything very clearly , Thank you very much.

[@fizXgirl314]

OH YEAH!! this helped me to find the next guess for use in the shooting method... LOVED IT!

[@walkingon2001]

thank for the video, it is very useful and easy to understand.

[@yzchenwei]

you suppose to check conditions and swap indexes if necessary.

[@adrees4u]

is it necessary that x0 be smaller than x1 or is it just a coincidence here? Furthermore how to decide which of the two initial x guess values to be assigned as x0 and x1?

[@numericalmethodsguy]

Not at all. 0 and 1 are subscripts, not a restriction on values of x0 and x1.

[@adrees4u]

@@numericalmethodsguy Got it. Thank you sir.

[@igonesyt]

Thanks from Brazil! You are awesome.

[@noora2053]

You are the best !!God bless you ()

[@Sitonyto]

I think your value for X2 is wrong, should have been 3.3553. Well, that's what i got.

[@Letmegoagainplease]

Good work sir and thank you, think you can do one for the succesive approximations method?

[@gog_magpie]

This is very helpful, thanks a lot :)

[@brucemendaros8079]

What is the name of the last process you did where you multiplied it with 100 to get the percentage? Thanks sir have a good day!

[@numericalmethodsguy]

It is the concept of absolute relative approximate error. See more here. nm.mathforcollege.com/topics/measuring_errors.html

[@brucemendaros8079]

Thank you sir, by the way, how did you get the initial values of x0 =4.0 and x1=5.5?

[@profautarkaw]

@@brucemendaros8079 Those are just guesses which I chose. Generally one uses physics of the problem to get initial guesses but this one is a generic problem.

[@lapitburaytitibuday]

dude! do yo have an example on fixed point iteration method? I'm looking around the internet and nothing gives me the exact meaning of it...

[@AKMautla]

beautifully explained. thank you!!

[@sunilp63]

@numericalmethodsguy what abt now??? fixed point...actually my professor dont know how to teach...after I saw ur lectures I became crystal clear...but I still have not understood fixed point and method of false positions..please post some videos..Thanks

[@CarlosDominguez-yr1ic]

Hi Sir. I Calculated X2 at the minute 4:52 of this video and I found that the value of X2 is 3.3553 which is different from the value of X2 shown in this video that is X2 = 3.353 Verification X2=X1-( f(x1)(X1-X0) ) / ( f(x1)-f(x0) ) X2=5.5-( (5.5^3-20)(5.5-4) ) / ( (5.5^3-20)-(4^3-20) ) X2=5.5-( (166.375-20)(5.5-4) ) / ( (166.375-20)-(64-20) ) X2=5.5-((146.375)(1.5))/(166.375-20-64+20) X2=5.5-219.5625/102.375 X2=5.5-2.144689 X2=3.355311 I did 7 iterations using Excel and I got the following results: Error (%) Xo= 4 X1= 5.5 X2= 3.355311355 63.91921397 (first iteration) X3= 3.05888392 9.690705592 (second iteration) X4= 2.779682997 10.04434404 X5= 2.721932852 2.121659417 X6= 2.71459513 0.270306338 X7= 2.714418107 0.006521558 X8= 2.714417617 1.80705E-05 Best regards from Venezuela. My name is Carlos Dominguez. I am a graduate student of specialization in Electric Power Systems at Universidad Central de Venezuela in Caracas.

[@hunterstubbs624]

Why is the error on your second iteration larger than the first?

[@whynot13]

I love you ! Cheers from UC San Diego

[@LShy3142]

So how'd you get so smart Buddy? Thx for the uploads. Much appreciated. :)

[@AnShiKa_sa]

I am not able to find any video on fixed point method ...

[@numericalmethodsguy]

Do not have one!

[@deepeshkushwaha4685]

how to calculate an approximate value for (4)(3/4){4 power 3 divided 4} using one step of secant method with x0=3 and x1=2

[@deathraiser2820]

how do you choose the inital guesses if they are not given in the question?

[@numericalmethodsguy]

You can use the physics of the problem. Assume you are trying to find the level to which a 3cm radius floating ball is submerged. You could use initial values somewhere between 0 and 6 cm. See example at mathforcollege.com/nm/mws/gen/03nle/mws_gen_nle_txt_secant.pdf

[@RobertoEmilioRomero]

Death Raiser best thing to do solving equations like these is to familiarize yourself withe the domain and co-domain AKA range of the function and graph it. Analyze the function. You can also graph them separate in the same viewing rectangles along with different transpositions of the function. At this point you must be familiar how to sketch functions if not graph them using a Computer Algebra System or CAS. There you can visually choose an interval of your choice to begin.

[@BilalChaudhary]

i can not find any video of "regula falsi method" i need that :(

[@RobertoEmilioRomero]

Bilal Chaudhary if you cannot find a specific video. Look for a PDF document of a text related to the topic.

[@lapitburaytitibuday]

Fixed point method pls..........

[@zezochi]

thank you very much teacher

[@mreriiie]

i have y=e^y + ln(y). Answer needs to have 3 correct decimals and i have to use the secant method, how do i proceed?

[@numericalmethodsguy]

+Mr. eriiie Rewrite as f(y)=y-e^y-ln(y)=0. Choose initial guesses and continue iterating till you find 3 decimal places coming out to be same. At any point the guesses cannot be negative as ln(-ve numbers) do not exist within real numbers.

[@CarlosDominguez-yr1ic]

Answer to Mr e. The results of using the secant method with initial guesses y0=0.5 y1=1 with an percent relative error less than 0.0001% is the following for the equation Y-Exp(Y)-ln(Y)=0 using Excel spreadsheet: n Yn Error % 0 0.5 │( x(i+1)-x(i))/x(i+1)│*100 1 1 2 0.319604301 212.8869032 (first iteration) 3 0.351205372 8.997889387 (second iteration) 4 0.3443491 1.9910818 5 0.344159898 0.054975036 6 0.344161287 0.0004037 7 0.344161287 8.03445E-08 Best regards from Caracas, Venezuela.

[@RobertoEmilioRomero]

I recommend change x for yor anyother variable of your convenience. The majority of students get intimidated with an equation like yours with Y in it. I will consider doing that first.

[@RobertoEmilioRomero]

I also strongly recommed you try first. Unless you cant do it and admit you dont know how to proceed. Ask someone how to proceed. Never take for granted that you can always ask someone on the internet to do it for you although they mostlikely will do because is fun for them and they know and love to solve problems. You need to be disciplined very well to be a great mathematician. Be realistic and first ask yourself "Am I capable of doing this?" If so never doubt yourself because if others can you can too. One day youll look back at a problem and tell yourself "I cant believe I didn't know how to solve such a relatively easy problem." And qhen I say relatively I mean relative to your age and educational level. Best,

[@khairulanuar2801]

Nice video..helped me so much..god bless u

[@RobertoEmilioRomero]

Khairul Anuar, God with a capital G. Hmmm!

[@Taiseerghulam2011]

Please sir i need ur help …i am an instructor in LIU... how u re arrange the the formula to get it from the similarity of two triangles ?

[@numericalmethodsguy]

autarkaw.wordpress.com/2013/10/01/reconciling-secant-method-formulas/

[@RobertoEmilioRomero]

An LIU instructor asking such question? Thats weird.

[@ashiskumarpanigrahi]

Plz solve the problem Use secant method to find out the root of the equation x3-4x-9 upto 3decimal digits

[@etornamtsyawo6407]

how are the initial guesses chosen?

[@numericalmethodsguy]

These are chosen randomly. If you know the physics of the problem, then that can help. See physical problems here. nm.mathforcollege.com/topics/secant_method.html

[@SANJANASINGH-gp3wh]

you are so good !!!!

[@EmeritusG]

does this come with free ring dings?

[@mczairutz01]

Thank you Sir. Mabuhay Philippines :)

[@Darzs_chidane]

oh i didn't know that, thanks for clearing that up

[@honest_review2492]

thank u so much it really help me alot

[@ozgurerbulan2097]

İngilizcene kurban sağol reyis büyüksün

[@Gl0bby]

This is Newtown methode with approximated derivate (instead of accurate one). Really doubt its Secant methode

[@rishav2708]

thank you so much Sir!!

[@dhananjayalakshan9389]

Thanks a lot sir...

[@benb.1114]

Thank you very much good sir! :)

[@saqlainramzan6640]

why 4 cube ?

[@skunkid2]

Thank you!

[@jorge19050]

very good, thanks!!!

[@ramana1-9-7-4]

Sir p/z explain falsi position method

[@numericalmethodsguy]

From my good colleague: nm.mathforcollege.com/chapter-03-06-false-position-method/

[@Gl0bby]

ohhh, so its basically combination of Euler and Newton Raphson.. that makes sense.. they didnt really need to have a special name for it though

[@ahmadwaheed2631]

Nice sir

[@n.a.4293]

thank you

[@hey_its_zae]

Thank you, sir :)

[@umutert]

cool stuff!

[@Sn1perBH]

thx

[@badz9308]

thanks

[@yubrajkarki.]

This is 100% wrong solution and function 4 and function 5.5 can't be taken

[@numericalmethodsguy]

You may be confusing secant method and false position method. The false position method (mathforcollege.com/nm/topics/false_position.html , a bracketing method, uses secant lines to estimate the root of an equation. The secant method (nm.mathforcollege.com/topics/secant_method.html , an open method (estimates do not need to bracket the root), uses secant lines to estimate the root of an equation. 23 ▼

[@mrodri63]

THX

[@hakkanimim6488]

alhamdolliah sir

[@Darzs_chidane]

regula falsi and secant method are the same

[@RobertoEmilioRomero]

chidane noppe. Not true. Dont confuse people.

[@ashandesilva7308]

thank u soo much :)

[@Kinggenton]

i need muller's method!

[@MKStudio-xs6mo]

how can i contact you sir

[@nabilalmarfadi7748]

dont expect him to answer u lol

[@bblinkshorts]

thnx

[@ozgunbzkrt]

nice pronunciation..

[@JoffreyB]

no word about concept where does this formula appeared at all. No graph, no explanation, just stupid using of formula. Dis

[@numericalmethodsguy]

Look at the link in the description that takes you to all resources in sequence. Better yet, for all resources, see below. Subscribe to the numericalmethodsguy channel, and go to MathForCollege.com/nm and MathForCollege.com/ma for more resources and share the link with your friends through social media and email. Support the site by buying the textbooks at www.lulu.com/shop/search.ep?keyWords=autar+kaw&type= Follow my numerical methods blog at AutarKaw.org. You can also take a free online course at www.canvas.net/?query=numerical%20method

[@RobertoEmilioRomero]

JOFFREY BARATHEON this guy already derived the formula in a prior video.

[@SchtekarnFU]

Damnit don't put the point in the center.. makes it look like multiplication

[@RobertoEmilioRomero]

SchtekarnFU lol. He puts it there because its understood. If you dont understand it, dont put the . in the center.