Newton's method function output.

Hello,

I have a little problem with Newton's method. I have the code and it is working but I would like to get the results such that I have the teration number n and the value of x_n according to it. Also I need the error and f(x_n) but I am only getting the x_n values on their own. The code is as follows

    function [x,n,err] = newton( f, dx, x0, tol, ITMAX )
    format long
    f= inline(f);
    dx = inline(dx);
    x(1) = x0 - (f(x0)/dx(x0));
    err(1) = abs(x(1)-x0);
    fx=feval(f,x);

    for n=2:ITMAX
    if (err(n-1) >= tol) & (n <= ITMAX)
        x(n) = x(n-1) - (f(x(n-1))/dx(x(n-1)));
        err(n) = abs(x(n)-x(n-1));
        n = n+1;
    else 
        break
    end
    end
  end

It would be nice if I could get the result in a table like this

   disp('_________________________________________________________________________________ ')
disp('         n               x_n              f(x_n)             error    ')
disp('_________________________________________________________________________________ ')
fprintf('\n')

However I am not quite sure how to use fprint command. Any help would be appreciated. Thank you.

Answer 1

[Jan]

The code contains several problems. E.g. you do not have to check for n < ITMAX inside the FOR loop, because the FOR itself limits n to this value already. The FOR cares for increasing n also, so omit n=n+1.

As the editor warnings show already, inline is deprecated. Use anonymous functions or function handles instead as inputs.

For fprintf:

% Before the loop:
fprintf('%10s%10s%10s%10s\n', 'n', 'x_n', 'f(x_n)', 'error');

% Inside the loop:
fprintf('%10g%10g%10g%10g\n', n-1, x(n-1), f(x(n-1)), err(n-1));

I suggest to switch to a while loop, because then you can update the values and the counter index n more consistently.

[Wojciech Zaremba]

Hi. Thank you for your answer, it really helps, just got one more question, I have noticed that when I use n-1 in second fprintf then MATLAB doesn't show the last value that it has calculated, when changed to just n then it will not show calculations for n=1, it is not a big issue but do you think it would be possible to include all n values in that table, staring from n=0? Thanks for the suggestions too.

Figured it out, thanks! :)