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Math Help - convergence

  1. #1
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    convergence

    can anyone show me...
    How do you prove that an iterative method is convergent??

    like for example if you have x_n = x_{n-1} - f(x_{n-1})/f'(x_{n-1})

    thank you
    Last edited by CaptainBlack; March 16th 2009 at 02:33 PM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by pandakrap View Post
    can anyone show me...
    How do you prove that an iterative method is convergent?? or like show that it converges some how

    like for example if you have y(k) = k - h(k)/h'(k)

    y(kn) = k(n+1)
    where this method is solving h(k) =0
    thank you
    Well this is Newtom-Raphson and its convergence depends on where you start and what h(x) actually is. See the Wikipedia article.

    CB
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  3. #3
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    Quote Originally Posted by pandakrap View Post
    can anyone show me...
    How do you prove that an iterative method is convergent??

    like for example if you have x_n = x_{n-1} - f(x_{n-1})/f'(x_{n-1})

    thank you
    You can't. It isn't always. Whether it converges of not depends on the function f, the set of possible values of f (obviously, if f(x)= x^2+ 1 where x is required to be real, this will not converge since it must converge to a solution of f(x)= 0 and x^2+ 1= 0 doesn't have a real solution) and, even when f is such that it can converge, whether it will or not depends on the initial choice of x_0.
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