# higher order newton iterations

**Jason Moxham
**
J.L.Moxham@maths.soton.ac.uk

*Sat, 2 Nov 2002 02:43:40 +0000*

Some examples of higher order convergence for newton iteration can be fou=
nd=20
here
http://numbers.computation.free.fr/Constants/constants.html
Has anyone tried any of these higher methods ? are they faster ?
Although there are less iterations , there are more multiplications , so =
it=20
not clear if they are better. Its fairly easy to do a count of the number=
of=20
ops required , so has anyone tried it ? The main problem is the rigourous=
=20
error anaylsis for tight bounds (which is beyond what I'm willing to do).=
For=20
the p-adic case , the error anaylsis is trivial .