Formatting code to display multiple results.

So, I'd like to alter the following code which I have written (Newton's Method), so that it not only outputs the final approximation of the root but each approximation for each iteration of the method. See what I'm saying? How would you suggest that I do this so that it's displayed somewhat neatly in the command window?

function xn = Newton (f, df, xi, tol)
xo = xi; 
xn = xo - f(xo)/df(xo); 
k = 0; 
while ((abs(xn - xo))/(abs(xn)) > tol) 
    if (k <= 100) 
        xn = xo - f(xo)/df(xo); 
        k = k + 1; 
    else
        warning('Maximum number of iterations has been reached') 
        break;
    end
end

[David]

Using fprintf would be best, apparently. However, I have no clue how to use this for data formatting and the help section didn't do much to clear it up.

[sixwwwwww]

just make a matrix like this

fprintf('Iteration #: %f and approximation value:%f\n', k, xn);

Answer 1

[sixwwwwww]

Dear David, you can output iteration number and iteration values as follows:

function [xn, iterations] = Newton (f, df, xi, tol) % output parameter "iteration" store iteration number and iteration values in cell array
xo = xi; 
xn = xo - f(xo)/df(xo);
k = 0; 
while ((abs(xn - xo))/(abs(xn)) > tol) 
    if (k <= 100) 
        xn = xo - f(xo)/df(xo); 
        k = k + 1;
        iteration{k, 1} = k;
        iteration{k, 2} = xn;
    else
        warning('Maximum number of iterations has been reached') 
        break;
    end
end

I hope it helps. Good luck!

[David]

Thanks, off topic but is there a problem with my code above? Should I be assigning xn to xo at the start of each iteration of the loop?

[sixwwwwww]

Yes you should replace xo with previous value of xn at each iteration. the other way to solve display problem is that you can store all iteration results in one matrix and display them using

disp

before end of your function

[David]

Fixed, Thanks.

[sixwwwwww]

You are welcome