Re: REPOST: Re: Flies in the ointment.

From: Tim Peters (tim.one_at_comcast.net)
Date: 03/17/05 

Date: Thu, 17 Mar 2005 18:42:37 -0500

...
[Tim Peters]
>> I also stumbled into this amazing scam on Wikipedia:
>>
>> "John Gabriel's Nth root algorithm"
>> http://en.wikipedia.org/wiki/John_Gabriel%27s_Nth_root_algorithm
>>
>> Nothing wrong with the algorithm,

[Nora Baron]
> The Gabriel algorithm says the iterations are defined by
>
> s_(i+1) = ((s_i)^(x/(n - 1)) + (n - 1) s_i)) / n,
>
> which seems a little silly.

Maybe this is browser-dependent. When I look at that page, it's "clearly"
s_i/(x^(n-1)) instead. Which is why I said what I said <wink>.

If you look at the history of the page, the original version was ASCII art,
and not open to this misinterpretation (well, not in a fixed-width font
anyway); this is cut-and-paste from page's first revision:

               x
           --------- means x divided by
               (n-1) s ^(n-1)
   s = s + (n-1)*s i
    i+1 i i
           ---------------------- (2)
                        n

[...]
> A straightforward implementation of Newton's method to solve
>
> y^n = x
>
> is simpler and requires only that you can compute integer powers,
> rather than roots.

That's what I said:

>> but it's just a clumsily-stated direct application of Newton's method
>> to finding a zero of f(y) = y^n-x (iterate y <- y - f(y)/f'(y)).

I think there's nothing here but a misunderstanding.

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