[Fwd: Re: improved Matrix.times()]

[Ron Boisvert <boisvert@nist.gov>]

-------- Original Message --------
Subject: 	Re: improved Matrix.times()
Date: 	Fri, 23 May 2008 11:29:50 -0400
From: 	Tim Poston <tim.poston@gmail.com>
Reply-To: 	tim.poston@gmail.com
To: 	boisvert@nist.gov
References: 	<4836D9F0.9010401@nist.gov>



Apart from the details of how to handle Single Value Decomposition
for truly humongous matrices, it's worth a second look at the scientific
reasons for even trying to, in the particular problem at hand.
With that many variables, I would first ask whether the system
is truly linear enough for SVD to be relevant in the first place --
higher order terms could so easily swamp it.
How sensitive is the answer to noise,
and how much noise can you (in this application) expect?
More broadly, how good are the data?

Vast algebraic manipulations, used without a strong theoretical rationale,
are easily subject to "Garbage In, Garbage Out".
Expecting SVD to act as a magic garbage filter
sometimes works on smaller problems, but vast ones?

Tim Poston
Bangalore