You want to use this method to find a point where \(f(p) = p \). In other words, the point you put into the function returns the same point. To put it in another perspective, when the line \(y = x \) intersects your function \(f(x)\).
INPUT initial approximation p_o;tolerance TOL; maximum number of iterations N
OUPUT approximate solution p or message of failure.
Step 1 Set i = 1.
Step 2 While i =< N do Steps 3-6
Step 3 Set p = g(p). (Compute p_i)
Step 4 If |p - p_o| < TOL then
OUTPUT (p); (Procedure was successful)
STOP.
Step 5 Set i = i + 1
Step 6 Set p_o = p (Update p_o)
Step 7 OUTPUT ('The method failed after N iterations'); (Failed procedure)
STOP