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Math Help - fixed point method

  1. #1
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    fixed point method

    if there is a function g(x)=sqrt(1+x^2) which satisfies all assumptions of fixed point method but still this iteration does not converge to any root why?

    i tried it by solving x(n+1)=g(x(n)) but i am getting x cancelled and left out eqn as 0=1 . what is the correct approach

    please help?
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  2. #2
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    Re: fixed point method

    Quote Originally Posted by prasum View Post
    if there is a function g(x)=sqrt(1+x^2) which satisfies all assumptions of fixed point method but still this iteration does not converge to any root why?

    i tried it by solving x(n+1)=g(x(n)) but i am getting x cancelled and left out eqn as 0=1 . what is the correct approach

    please help?
    where are you getting g(x) from? does $g(x)=x-\frac{f(x)}{f'(x)}$ for some $f(x)$ ?

    $f(x)=e^{\frac{1}{2} \left(-x \left(\sqrt{x^2+1}+x\right)-\sinh ^{-1}(x)\right)}$ satisfies this.

    Are you trying to find a root of this f(x)?

    since $g(x)>x~~\forall x \in \Re$ it's pretty clear that g(x) won't converge when iterated.
    Thanks from prasum
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