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!

Convergence Interval for Newton's Method

  1. Oct 3, 2011 #1
    1. The problem statement:

    In what region can we choose x0 and get convergence to the root x = 0 for f(x) = e-1/x^2

    2. Relevant equations
    xn+1 = xn - f(xn) / f'(xn)


    3. The attempt at a solution
    The only thing I've come across is a formula that says |root - initial point| < 1/M where M = max|f''(x)|/(2min|f'(x)| where x belongs to a "sufficiently small interval"

    My thought: [-1,1]
     
  2. jcsd
  3. Oct 3, 2011 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    The exponential function does not equal zero for any real argument, so there is NO root. (I suppose you could regard x = +-infinity as "roots", but things like |root - x_n| are then not real numbers, either.) If you regard the question as: "for what x_0 does x_n --> + infinity (or -infinity)?", then you might have a sensible question.

    RGV
     
    Last edited: Oct 3, 2011
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Convergence Interval for Newton's Method
Loading...