MATLAB：哈顿方法的牛顿法

Question

我有这个牛顿法的MATLAB代码，我试图为它编写一个修改版本来创建Halley的方法。代码是

function root = newton(fname,fdname, fd2name, x,xtol,ftol,n_max,display)
% Newton's Method.
%
% input:  fname is a string that names the function f(x).
%         fdname is a tring that names the derivative f'(x).
%         x is the initial point
%         xtol and ftol are termination tolerances
%         n_max is the maximum number of iteration
%         display = 1 if step-by-step display is desired,
%                 = 0 otherwise
% output: root is the computed root of f(x)=0
%
n = 0;
fx = feval(fname,x);
if display, 
   disp('   n             x                    f(x)')
   disp('------------------------------------------------------')
   disp(sprintf('%4d %23.15e %23.15e', n, x, fx))
end
if abs(fx) <= ftol
   root = x;
   return
end
for n = 1:n_max
    fdx = feval(fdname,x);
    d = fx/fdx;
    x = x - d;
    fx = feval(fname,x);
    if display, 
       disp(sprintf('%4d %23.15e %23.15e', n, x, fx)), end
    if abs(d) <= xtol | abs(fx) <= ftol
       root = x;
       return
    end
end
root = x;

我知道我必须更改for循环中的代码。

所以我改变了：

fd2x = feval(fd2name, x)

d = 2*fx*fdx/(2*fdx.^2 - fxfd2x)

这有意义吗？我还需要改变什么？