Peter Foelsche

2017-06-18 00:58:39 UTC

Assume that f(x) and x itself is a n-dimensional vector.

If one derives the newton method, we are dealing with a 2-dim Jacobian.

Can one derive this for Halleyâs method for vector valued functions?

I figured how to do this only for scalar functions:

n:2;

ratsimp(subst(f0, f(x), subst(f3, diff(f(x),x,3), subst(f2, diff(f(x),x,2), subst(f1, diff(f(x),x), n*''(diff(1/f(x),x,n-1))/''(diff(1/f(x),x,n)))))));

So â how to do this for x and f(x) being a vector?

Peter

If one derives the newton method, we are dealing with a 2-dim Jacobian.

Can one derive this for Halleyâs method for vector valued functions?

I figured how to do this only for scalar functions:

n:2;

ratsimp(subst(f0, f(x), subst(f3, diff(f(x),x,3), subst(f2, diff(f(x),x,2), subst(f1, diff(f(x),x), n*''(diff(1/f(x),x,n-1))/''(diff(1/f(x),x,n)))))));

So â how to do this for x and f(x) being a vector?

Peter