1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Newtons method

  1. Dec 8, 2006 #1
    so I was helping my friend today and ran into a problem.

    the problem was to use newtons method to approx. the intersection points of two graphs.

    f=x^2
    g=cosx

    so I subtracted f-g, found the derivative and pluged in some guesses.

    Except all of my guesses just blew upwards in values instead of zooming in on a point. whats the deal?

    Rob
     
  2. jcsd
  3. Dec 8, 2006 #2
    Your guesses were too far from the root. To ensure convergence, the distance between your initial guess and the root has to be less than [itex] 2 \delta \over M [/itex] where

    [tex]|f'(x)| \geq \delta > 0[/tex]

    [tex]|f''(x)| \leq M[/tex]

    for all [itex]x \epsilon [a,b][/itex] in the interval [itex][a,b][/itex] you're considering
     
    Last edited: Dec 8, 2006
  4. Dec 8, 2006 #3
    Your totally right. Thats one tight interval to make a guess for though. I was only about .2 away from a working guess. Thanks
     
  5. Dec 20, 2006 #4
    Hi Robierob,

    When u compute f(x)-g(x), u should get x² - cos x on which u can apply Newton's method. Actually u can ensure that your guess is not far from the actual root by finding when your function changes from positive to negative or vice versa. There will be a root when the function changes sign provided that it is continuous for the interval where the root lies. For example, there is a root between x=a and x=b when a and b are consecutive and f(a) f(b) < 0. U can deduce the values of a and b by substitution and use a starting value between a and b for your approximation. That should help u arrive at your root quickly.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Newtons method
  1. Newton's method (Replies: 10)

  2. Newtons method? (Replies: 2)

  3. Newton's method (Replies: 3)

  4. Newton's Method (Replies: 3)

  5. Newton method (Replies: 3)

Loading...