Newton's Method missing value

I wrote Newton's method to be

function [cVec,n] = Newtons_method(f,fp,x0,tol,nmax)

cVec = [];
cVec(1)=x0;
i=0;

while i <=nmax
    i=i+1;
    cVec(i)=x0;
    c = x0-(f(x0)/fp(x0));
    if abs(c-x0)<tol
        c=x0;
        break;
    else
        x0=c;
    end
end
n=i-1;
cVec=cVec';
end

and used the following to call it

f=@(x)(x.^2-3);
fp=@(x)(2.*x);
x0=2;
tol=10^-10;
nmax= 100;
[c,n]=Newtons_method(f,fp,x0,tol,nmax)

From this, I get a [5,1] column vector but I'm supposed to get a [6,1] vector. I've messed around with the placement of certain lines of code and indices, but haven't gotten the desired result.

Thanks in advance.

Answer 1

[Torsten]

If n is the number of Newton steps, you must start with n = 0 instead of n = 1 in "Newtons_method".

I counted the number of Newton steps + the initial value, thus the length of the array cVec.

f = @(x) x.^2-3;
fp = @(x) 2.*x;
x0 = 2;
tol = 10^-10;
nmax = 100;
format long
[c,n] = Newtons_method(f,fp,x0,tol,nmax)

c = 6×1

2.000000000000000 1.750000000000000 1.732142857142857 1.732050810014728 1.732050807568877 1.732050807568877

n = 
     6

function [cVec,n] = Newtons_method(f,fp,x0,tol,nmax)
  cVec(1) = x0;
  n = 1;
  while n <= nmax
    c = x0 - f(x0)/fp(x0);
    n = n+1;
    cVec = [cVec;c];
    if abs(c-x0) < tol
        break;
    else
        x0 = c;
    end
  end
end