1. Limited time only! Sign up for a free 30min personal 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!

Accelerated newton method

  1. Aug 22, 2011 #1
    1. The problem statement, all variables and given/known data
    given [tex] f \in C^2 [/tex] such that [tex] f(a)=f'(a)=0 ^f''(a)\neq 0 [/tex] prove that the modified newton method [tex] x_{n+1}=x_n-2 \frac{f(x_n){f'(x_n)} [/tex] coverges with order two.

    2. Relevant equations
    if g(x) is an iterative function such that the first m derivatives of g at a are zero and [tex]g^{(m+1)}\neq 0 [/tex] then the order of convergence is m+2

    3. The attempt at a solution

    So it seems that i want to show that my iterating function [tex] g(x)=x-2 \frac{f(x){f'(x)} [/tex] satisfies [tex] g(a)=0 ^ g'(a)\neq 0 [/tex]
    But using le'hospitals rule to find g(a) i have [tex] g(a)=a-2\frac{f'(a)}{f''(a)}=a \neq 0 [/tex]
    Whats wrong here?
    Last edited by a moderator: Aug 22, 2011
  2. jcsd
  3. Aug 22, 2011 #2


    Staff: Mentor

    Fixed your LaTeX. I'm assuming that you were using the symbol ^ to mean "and."
  4. Aug 22, 2011 #3


    Staff: Mentor

    Did you calculate g'(x)? You will need g'(x) so that you can evaluate g'(a). I'm not sure why you think you need L'Hopital's Rule.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Accelerated newton 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)