This method is used to find a point \(p\) where \(f(p) = 0\). In other words, where the rate at which your function \(f(x)\) changes is zero. Or you can think of it as where the function touches the x axis.
INPUT initial approximation p_o;tolerance TOL;maximum number of iterations N_o
OUTPUT approximate solution p or message of failure.
Step 1 Set i = 1.
Step 2 While i =< N_o do Steps 3-6
Step 3 Set p = p_o - f(p_o)/f'(p_o). (compute p_i.)
Step 4 If |p - p_o| < TOL then
OUTPUT (p); (The 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_o iterations')
(The procedure was unsuccessful)
STOP