Cube Root Algorithm in Matlab
This program is the newton raphson iteration to approximate a root
%Input - f is the object function input as a string 'f'
% df is the derivative of f input as a string 'df'
% p0 is the initial approximation to a zero of f
% delta is the tolerance for p0
% epsilon is the tolerance for the function values y
% max is the maximum number of iterations
% output -p0 is the newton raphson approximation to the zero
% err is the error estimate for p0
% k is the number of iteration
% y is the function value f(p0)
of f(x)=0 given initial approximation p0 and using the iteration,
pk= pk-1 - ( f(pk-1)/ f'(pk-1) ) for k = 1,2,3 ....
Note... k and k-1 are in subscripts of p