higher order newton iterations

[Jason Moxham]

Some examples of higher order convergence for newton iteration can be fou=
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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 =
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not clear if they are better. Its fairly easy to do a count of the number=
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ops required , so has anyone tried it ? The main problem is the rigourous=
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error anaylsis for tight bounds (which is beyond what I'm willing to do).=
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the p-adic case , the error anaylsis is trivial .