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Homework Help: 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

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    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
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