How do you solve fixed point iteration method?

To solve a problem using the fixed-point iteration method, you first need to rearrange the equation ( f(x) = 0 ) into the form ( x = g(x) ). Next, you select an initial guess ( x_0 ) and compute subsequent approximations using the formula ( x_{n+1} = g(x_n) ). This process is repeated until the changes between consecutive iterations are sufficiently small, indicating convergence to a fixed point. It's important to ensure that the function ( g(x) ) fulfills the conditions for convergence, such as being a contraction mapping.