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From: markh@csd4.csd.uwm.edu (Mark William Hopkins)
Newsgroups: comp.ai.neural-nets
Subject: Re: Backpropagation with Newton's Method, and recurrence.  Source code.
Message-ID: <7937@uwm.edu>
Date: 29 Nov 90 03:19:36 GMT
References: <1248@helens.Stanford.EDU> <7684@uwm.edu> <3146@exodus.Eng.Sun.COM>
Sender: news@uwm.edu
Organization: University of Wisconsin - Milwaukee
Lines: 17

In article <3146@exodus.Eng.Sun.COM> landman@hanami.Eng.Sun.COM (Howard A. Landman) writes:
>>In article <1248@helens.Stanford.EDU> wan@isl.Stanford.EDU (Eric A. Wan) writes:
>>>You mention the method does not work well for f(x) = x^2.  In fact, Newton's
>>>Method applied to the gradient of x^2 converges in one step.
>
>In article <7684@uwm.edu> markh@csd4.csd.uwm.edu (Mark William Hopkins) writes:
>>You lost me here.  Try using Newton's method to find a zero of x^2.
>
>The gradient of x^2 is 2x.

Hence the iteration formula:

	      x[n+1] = x[n] - f(x[n])/f'(x[n]) = 1/2*x[n].

So Newton's Method applied to x^2 converges only as slowly as the Method of
Bisection.  The original article wasn't talking about using Netwon's Method
on the gradient of x^2, but on x^2.