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Math Help - you're a god if you can prove this

  1. #1
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    you're a god if you can prove this

    Let f be some given function for which we wish to find a such that
    f(alpha)= 0. Suppose that the equation f(x)= 0 may be arranged into
    the form x=g(x), such that for some interval (a,b) alpha is in (a,b) and
    g(x) belongs to (a,b) . Further, suppose that g is differentiable with |g'(x)|</= C
    for x belonging to (a,b), where C is some positive number. (Note that x=g(x)
    implies that alpha=g(alpha) If we have the iteration method
    Xn+1=g(Xn)
    where X0 belonging to (a,b) is some given value, prove that
    |alpha - Xn+1| </= C|alpha - Xn|

    please note that when i say "belonging to" i mean that symbol that looks a bit like an 'E'
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  2. #2
    Forum Admin topsquark's Avatar
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    Re: you're a god if you can prove this

    Quote Originally Posted by limpfisch View Post
    Let f be some given function for which we wish to find a such that
    f(alpha)= 0. Suppose that the equation f(x)= 0 may be arranged into
    the form x=g(x), such that for some interval (a,b) alpha is in (a,b) and
    g(x) belongs to (a,b) . Further, suppose that g is differentiable with |g'(x)|</= C
    for x belonging to (a,b), where C is some positive number. (Note that x=g(x)
    implies that alpha=g(alpha) If we have the iteration method
    Xn+1=g(Xn)
    where X0 belonging to (a,b) is some given value, prove that
    |alpha - Xn+1| </= C|alpha - Xn|

    please note that when i say "belonging to" i mean that symbol that looks a bit like an 'E'
    What have you been able to do so far?

    -Dan
    Thanks from Draco93
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