Newton's Method implementing in Matlab

Hi everyone,

This weeks task in our course "numerical methods" we have to implement a Newton's Method following the given instruction:

    % function x=newton(x0,F,DF,nMax,TOL)

 %starting point and Value of F in the starting point.

 x = x0;
 Fx_new = F;

 %Newton iteration
 for ii = 1:nMax

    %value of F and DF in the old iteration
    Fx = Fx_new;
    DFx = DF;

    %condition, DF not zero
    if abs(DFx)<1e2*eps
        fprintf('DFx ist zu klein\n')
        assert(false);
    end

    %Newton update
    delta_x = fx/DFx;

    %new iterate
    x = x-delta_x;

    %value of F in the new iterated
    Fx_new = Fx;

    %if update too small -> stop and exit
    if abs(DFx\Fx_new) < TOL;
        break
    end
end

However, it doesnt work. I'm not quite sure how to handle F at position x0 and how to the new iterated for F. It would be most kind if someone would help me.

Kind regards

Jean-Marc

Answer 1

[Geoff Hayes]

Jean-March - I suspect that the inputs F and DF are function handles to the function and its first derivative. For example,

 f  = @(x)x^2 + 3*x;
 df = @(x)2*x + 3;

where df is the first derivative of f. As these are function handles, we can evaluate them for any value of x. For example, if x is 42, then we can write

 f(42)
 df(42)

to evaluate f and df are 42. For Newton's Method, you would use these two functions as

 xnl = xn - f(xn)/df(xn);

where xn is the value calculated on the previous iteration (or x0 if first the first iteration).

Please be careful when naming your variables - you attempt to use an fx but it is never assigned. Should this be Fx instead? Also, is delta_x an appropriately named variable?

Try implementing the above into your code and see what happens!