function u = mysqrt(a)
%compute fifteen approximations to square root of a
%using Newton's method. 

%In order to study the result, we collect two columns of information.
%the first column will hold the approximations to the square root of a.
%The second column will hold the error, that is the difference between
%the square root computed using matlab's sqrt function and the value
%from Newton's method. 

u=zeros(15,2);
u(1,1)=a; %We use a as the initial guess.

for j = 2:15;
u(j,1)  = 0.5*(u(j-1,1)+a/u(j-1,1));
end

%In the statement below, : refers to the entire column.
u(:,2)= abs(sqrt(a) -u(:,1));

end

%---------------------end file--------------
Output from above file. 

>> format long e
>> mysqrt(5)

ans =

     5.000000000000000e+00     2.763932022500210e+00
     3.000000000000000e+00     7.639320225002102e-01
     2.333333333333333e+00     9.726535583354368e-02
     2.238095238095238e+00     2.027260595448332e-03
     2.236068895643363e+00     9.181435736138610e-07
     2.236067977499978e+00     1.882938249764265e-13
     2.236067977499790e+00                         0
     2.236067977499790e+00                         0
     2.236067977499790e+00                         0
     2.236067977499790e+00                         0
     2.236067977499790e+00                         0
     2.236067977499790e+00                         0
     2.236067977499790e+00                         0
     2.236067977499790e+00                         0
     2.236067977499790e+00                         0

>> 2.236067977499790e+00 * 2.236067977499790e+00

ans =

     5.000000000000001e+00