Re: Flies in the ointment.

From: r.e.s. (r.s_at_ZZmindspring.com)
Date: 03/17/05 

Date: Thu, 17 Mar 2005 03:25:02 GMT

"Tim Peters" <tim.one@comcast.net> wrote ...

> 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, 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)). This certainly doesn't go under the name of "John
> Gabriel" in any numerical analysis circles I've run in <heh>.

Surprisingly, it's cited at
http://www.cs.princeton.edu/introcs/96optimization/
which seems not to recognize it as an application of Newton's Method.
It is somewhat interesting that the recurrence relation has been
written in the form of an *average* (shades of an "average tangent"?).

This post is even more interesting ...
http://mathforge.net/index.jsp?page=seeReplies&messageNum=635
  "There are infinitely many numbers between 0.999.. and 1
  [...] My name is JOhn Gabriel and I am on a crusade [...]
  Why not call 0.999... what it really is - an irrational
  like 1/3, pi, e or sqrt(2)."

Relevant Pages

  • Re: Surrogate factoring, basic algorithm
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  • Re: Surrogate factoring, corrected algorithm
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  • Re: Surrogate factoring, corrected algorithm
    ... Tim Peters wrote: ... I get a mere 24960 gcd trials. ... > some j, so at least one of {proof, algorithm, implementation} is wrong. ... I never saw a proof of the claim that one of the GCD's must be a proper ...
    (sci.crypt)
  • Re: I was right, surrogate factoring proof
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    (sci.crypt)