I started with 3.0 as an initial guess just to solve the problem. You could start with any guess you want. The root may diverge or converge. In many physical problems, the physics of the problem may help you with a good initial guess.
A very great lesson. I am just learning about the absolute relative error for the first time, and I hope to pass it on, share, with my course mates. Thanks a lot
thank you sir, actually i didn't attend classes in my college now for finals i dnt know nothing , from u videos i got to know lots of things abt numerical thank u once again
@dmwirichia You are partially right. You should get 0.037%. The number 0.009% was obtained using more significant digits in the calculations of the roots.
One only takes first derivative in Newton-Raphson method. There are modifications proposed to the Newton-Raphson method when the equation has repeated roots, which involve taking derivative of f(x)/(f'(x).
@Jodisbear That is an initial guess to get the procedure started. To make an estimate of the initial guess, you may look at the physics of the problem. For that, read by going to numericalmethods(dot)eng(dot)usf(dot)edu, click on Newton Raphson Method and see the textbook chapter example.
@AshimHybrid07 Well take the derivative of x^3-x-1, that is 3x^2-1. Now use an initial guess like x0=2 or so in the setup and you are on the way. When the fourth decimal place does not change in the iterations, you have achieved your result. The answer is 1.3247. The eqn has two complex roots too, but those cannot be found by NR method. For that you need to use methods such as Muller's method.
@frilink That is an initial guess to get the procedure started. To make an estimate of the initial guess, you may look at the physics of the problem. For that, read by going to numericalmethods(dot)eng(dot)usf(dot)edu, click on Newton Raphson Method and see the textbook chapter example.
Yes, till the time the function f(x) in f(x)=0 equation is differentiable and continuous in the domain of the values of x used, you can use it for any equation of the form f(x)=0.
@SnakeEater1912 The exercises are given at the numerical methods website for which the URL is at the numericalmethodsguy channel. Go to keyword, and then to multiple-choice.
@IgoruCafekko That is the first derivative of the function f(x)=x^3-20 with respect to x. How did I get that? Go to numericalmethods(dot)eng(dot)usf(dot)edu and click on Keyword. Click on Newton Raphson method. You can also click on Primer on Differentiation if you need brushing up on differential calculus!
3rd iteration's absolute value approx. error is not 0.009%... Ive done it 3 times now and I'm getting an approx error of 0.0368% am i wrong? I know no big deal... Your videos are great! Thank you!
Is there any other way of finding initial guesses instead of drawing the graph? By the way, nice video Sir. I really appreciated it, very easy to understand. Thanks.
That is an initial guess to get the procedure started. To make an estimate of the initial guess, you may look at the physics of the problem. For that, read by going to numericalmethods(dot)eng(dot)usf(dot)edu, click on Newton Raphson Method and see the textbook chapter example.
That is an initial guess to get the procedure started. To make an estimate of the initial guess, you may look at the physics of the problem. For that, read by going to nm(dot)mathforcollege(dot)com, click on Newton Raphson Method and see the textbook chapter example.
Example: To find to what depth a ball is floating in water results in a cubic equation. In this case we know that the depth has to be between zero and the value of the diameter of the ball. So choosing half the diameter is a good guess. Do a Google search on STEM numerical methods. Go to the first site that shows up. Click on Keyword. Go to Newton Raphson Method. Click on Textbook notes to see the example.
thanku sir....me ajay...really glad....for getting ur knowledge. ...your all video help me a lot....for understanding the concept.....thanku...sir...u ar best😊
@tamilselvi90 That is an initial guess to get the procedure started. To make an estimate of the initial guess, you may look at the physics of the problem. For that, read by going to numericalmethods(dot)eng(dot)usf(dot)edu, click on Newton Raphson Method and see the textbook chapter example.
Thank you for making such a good video. You are much better than my lecturer, I wish I can download your video so that I can watch it over and over again without log in to youtube. Do you have exercises that I can try?
@00jklr First all equations to be solved by NR method have to be put in f(x)=0 form (Do you know why). So f(x)=x^2-4*cos(x)=0. f ' (x)=2*x+4*sin(x). So x(i+1)=x(i)-(x(i)^2-4*cos(x(i))/(2*x(i)+4*sin(x(i))) Read by going to numericalmethods(dot)eng(dot)usf(dot)edu, click on Newton Raphson Method and see the textbook chapter
Hello sir, What we need to do when our function is trignometric? should we use any integer value as our intial guess or we need to take radian angle as our intial guess? Your videos are really good. Kindly request you to answer.
Hello: When you have a trigonometric function, the arguments are always radians. They are never any other unit of angle. If you have an equation like x*sin(x)-3+x^2=6, and even if someone tells you that initial guess is 60 degrees, you have to convert the value to radians. An initial guess can be an educated guess based on the physics of the problem and it does NOT have to be an integer.
@arseneok1 If one knows something about the physics of the problem, that could be used as a basis for an initial guess. Go to numericalmethods(dot)eng(dot)usf(dot)edu and click on Newton Raphson method. Then click on the textbook chapter pdf file and you will see how the physics of the problem is used to assume an initial guess.
I've also haerd that you can use the newton raphson method combined with the shooting method in order to make your next initial condition guess. Do you have any good resources on how this can be done? I'm attempting it on an assignment. Your lectures are great!
thank u it's so helpful , i just want to ask about somthing called " newton raphson rule for multiple roots" that has this form : Xi+1 = Xi -(( f . f ` ) / ( f `^2 - f `` . f ) ) ,when do we have to use it insted of the rule that u mentioned in the exapme ?
that was really helpful but i'm looking for applications of newton raphson method for equipments like heat exchanger or reactors ??where should i start thanks in advance
@vitalcoordinates All your prof is trying to do is to start with a good initial guess, and "almost" ensure that you end up finding the root you are looking for. Go to numericalmethods(dot)eng(dot)usf(dot)edu and click on Keyword. Click on Newton Raphson method. Read the N-R method textbook chapter.
Respected Sir, Thank you very much for Newton Raphson Method can u please post Bairstow Method...i've been behind it since few days n its kinda becumin a maze for me..please can you help me...
For those asking about the initial guess, it doesn't matter what you choose. The only thing to keep in mind is that the further your guess is from the actual root, the more iterations of the method you will need to get to an accurate result
sir,as the equation is a very easy one,we can easily guess the root to be 3....but when the equation would be a certain difficult one,in that case how can i make the initial guess??
To make an estimate of the initial guess, you may look at the physics of the problem. See examples at nm.mathforcollege.com/topics/newton_raphson.html Go to physical problems as well as look at the example in mathforcollege.com/nm/mws/gen/03nle/mws_gen_nle_txt_newton.pdf
+Nupur Vishnoi f(x)=x^3-20 f'(x)=d/dx(x^3-20)=3*x^2. Comes from formula d/dx(x^n)=n*x^(n-1) www.khanacademy.org/math/differential-calculus/taking-derivatives/power_rule_tutorial/v/proof-d-dx-x-n
Sir X0 value is taken as 3 But by intermediate value theorem it is not supported Because f(3)=7 f(4)=44 There is no change of sign Can anybody clear this doubt
Read or watch content at nm.mathforcollege.com/topics/measuring_errors.html . To find how many significant digits we can trust in our solution, we compare the abs rel approx error to a pre specified tolerance. If the pre specified tolerance is 5%, one significant digit can be considered to be at least correct, if it is 0.5%, then 2 significant digits can be considered at least correct, and so on. Read the content at the link and you will be all set.
That is an initial guess to get the procedure started. I just chose it from looking at the equation. To make an estimate of the initial guess, you may look at the physics of the problem. For that, look at some examples where we have taken advantage of that. Go here mathforcollege.com/nm/mws/gen/03nle/mws_gen_nle_txt_newton.pdf and also look at nm.mathforcollege.com/topics/newton_raphson.html and then look for "EXAMPLES FROM OTHER MAJORS"
Thank you. To get even more help, go to MathForCollege.com/nm and MathForCollege.com/ma for more resources and share the link with your friends. Follow my numerical methods blog at AutarKaw.org. You can also take a free online course at www.canvas.net/?query=numerical%20methods
sir, can you help me in this question..... i m understand how to solve it.....i solved other questions of N-R method..... but now facing prob in this question. x^3-x-1=0 -four decimal places
Sorry sir. My question in secant method when u drived the formula geometrically …how u rearrange the terms from the similarity of two triangles to the formula …?
Why is it that for the 3rd iteration when I do it I get 0.37% for my relative approx. error? I do it just as Ea= [(2.714-2.715)/2.714] * 100 and I get .37%. I double checked with multiple calculators yet I am puzzled as how you got .009%. Can you please explain or anyone do the math at 8:12 in the video and tell me how you got it. Thaks
Sir you said that an approximation is correct to at least 3 significant digits when the relative approximate error=0.0009% is smaller than 0.05%(at 9:26 in the video).Is there any proof for that theorem? I watched all your classes up to now and I could not see any proof for that theorem. Did I miss something? Could you please explain the derivation of this theorem or at least tell me where can I find it? Thank you in advance.
Hello: It is not explained in the book. The proof is here though and you will need to understand binary representation and floating point representation to follow it. math.stackexchange.com/questions/180252/why-does-relative-error-give-number-of-correct-digits
