Re: REPOST: Re: Flies in the ointment.

From: Tim Peters (tim.one_at_comcast.net)
Date: 03/18/05 

Date: Thu, 17 Mar 2005 19:05:31 -0500

[Randy Poe]
>> I notice that somebody has made a
>> comment that it's Newton's method. Think I'll take a
>> stab at editing and retitling the article tonight
>> and see what happens.

[r.e.s.]
> Please see also my comment that it is a simple fixed-point iteration
> obtainable without Newton's method.

Don't you think that's a stretch, though? I do, for two reasons:

1. General. A zero r of a function f(x) is always a fixed point of a
   Newton-method iteration (well, assuming f'(r) is defined). Deriving
   the same formula from a fixed-point perspective may be an exercise
   in cleverness, but if you can get the same thing directly from
   applying Newton's method, the latter is preferable because entirely
   straightforward.

2. Specific. You can find the n'th-root Newton method all over the
   web, in its weighted-average and "raw" forms. Heck, it's frequently
   given as a programming assignment in intro numerical analysis
   courses. In these contexts, it's always presented as an application
   of Newton-Raphson (proof: I looked at a lot of course handouts
   Google could find <wink>).