Cube Root Algorithm in Matlab

Code:

`function[p0,err,k,y]=newton(f,df,p0,delta,epsilon,max1)`

%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)

for k=1:max1

p1=p0-feval(f,p0)/feval(df,p0);

err=abs(p1-p0);

relerr=2*err/(abs(p1)+delta);

p0=p1;

y=feval(f,p0);

if (err<delta)|(relerr<delta)|(abs(y)<epsilon),break,end

end

This program is the newton raphson iteration to approximate a root

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