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From: loren@tristan.llnl.gov (Loren Petrich)
Newsgroups: comp.ai.neural-nets
Subject: Do I Understand Conjugate Gradients Now?
Message-ID: <68144@lll-winken.LLNL.GOV>
Date: 18 Sep 90 06:50:13 GMT
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Organization: Lawrence Livermore National Laboratory
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Originator: loren@tristan


	After reading _Numerical Recipes_, I think I understand what
Conjugate Gradients are now.

	Let us say one wants to minimize a function f(x). Given a
starting point x, one knows that the negative of the local gradient, g
= - grad f(x) will lead one to the minimum. So one finds f(x+g*l),
where l is some scalar greater than zero, and tries to minimize it as
a function of l. This is a one-dimensional problem, which is a lot
easier than a multi-dimensional one. Alternately, if one knows only
the gradient, one can look for when g*(- grad f(x+g*l)) changes sign
as one increases l.

	One repeats this step as many times as necessary to achieve
convergence. I presume that it can be shown that it will always find a
local minimum. Is that correct?


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Loren Petrich, the Master Blaster: loren@sunlight.llnl.gov

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