% This MATLAB code performs Newton's method based on the user.
%  The user specifies either the number of iterations to perform
%  or the error tolerance.  See Section 4.9 of Stewart for details.

stop=input(' Enter number of iterations or error tolerance--> ');
if stop>1,
    num_steps = stop;    % Perform a specified number of iterations
else
    tolerance = stop;    % Iterate until error tolerance reached
end
x1 = input(' Enter the initial condition, x1--> ');

x = [x1];
xn = x1;
if stop>1,               % Perform a specified number of iterations
    for i=1:num_steps,
        xnext = xn - (xn^3-xn^2-1)/(3*xn^2-2*xn); % #6 section 4.9
        x = [x; xnext];   % keep history of the estimates
        error = xnext-xn; % calculate the difference between consec terms
        xn = xnext;
    end
    xnext  % display the final estimate
    error  % display the difference between the last two estimates
else
    done = 0;  % iterate until error tolerance met
    steps = 0;
    while done==0,
        xnext = xn - (xn^3-xn^2-1)/(3*xn^2-2*xn); % #6 section 4.9
        x = [x; xnext];  % keep history of the estimates
        if (abs(xn-xnext)<tolerance), % determine if the est. is w/in tolerance
            done=1;
        end
        steps = steps+1;   % count the number of steps
        xn = xnext;
    end
    xnext   % display the final estimate
    steps   % display the number of iterations it took
end