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MathGroup Archive 1996

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Re: Biggest eigenvalues for a huge matrix

  • To: mathgroup at smc.vnet.net
  • Subject: [mg4142] Re: Biggest eigenvalues for a huge matrix
  • From: siegman at ee.stanford.edu (A. E. Siegman)
  • Date: Fri, 7 Jun 1996 02:07:50 -0400
  • Organization: Stanford University
  • Sender: owner-wri-mathgroup at wolfram.com

>  > I am interested in calculating eigenvectors (and eigenvalues) for,
>  > say, 300x300 matrix. I need just a few (three or four) of the biggest
>  > eigenvalues.  In this order, Eigenvalues and Eigenvectors seem not be
>  > efficient, so I want to write some code.  


   For a quick and dirty approach, you could just implement what's known
in the optical resonator field as the "Fox and Li" method (in essence,
just repeated multiplcation of an arbitrary input vector by the matrix),
possibly supplementing this by the "Prony method".  There's a vast
literature on the subject.  I certainly didn't originate it, but for a
description you could start with my LASERS text (University Science Books,
1986, or A. E. Siegman and H. Y. Miller, "Unstable optical resonator loss
calculations using the Prony method," Appl. Opt. 9, 2729--2763 (December
1970), and work backwards.

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