Fixed Point Iteration Method Can anyone explain or prove the Fixed Point Iteration method? 
I know the conditions of fixed point existence.
A fixed point is a point of a function ${f}$ on a continuous interval ${(a,b)}$ which satisfies this condition : ${x=f(x)}$, But i don't know how to conclude this method :${{x}_{n+1}=f(x_n)}$

The Fixed Point Iteration Method takes an equation
$$f(x)=0$$
and converts it into the form
$$x=g(x)$$
You then make an initial guess, say $x_0$, and recursively compute $$x_{n+1}= g(x_n)$$
Continue this process until one of the following criteria is met:


*

*A specific number of iterations are done (which you define yourself)

*The error $E= | x_{n+1}-g(x_n)| \leq \epsilon$, where $\epsilon$ is the degree of accuracy which you prefer.

