# Math Help - fixed point method

1. ## 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?

2. ## Re: fixed point method

Originally Posted by prasum
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.