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Re: Documentation of Eigenvalues[], Eigensystem[]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg114223] Re: Documentation of Eigenvalues[], Eigensystem[]
  • From: Roman <rschmied at gmail.com>
  • Date: Sat, 27 Nov 2010 03:47:55 -0500 (EST)
  • References: <icdo32$68p$1@smc.vnet.net> <ico27c$nla$1@smc.vnet.net>

On Nov 26, 11:30 am, Peter Pein <pet... at dordos.net> wrote:
> Am Mon, 22 Nov 2010 12:35:46 +0000 (UTC)
> schrieb Murray Eisenberg <mur... at math.umass.edu>:
>
> > This is definitely a gap in the documentation.
>
> > To find out that Eigenvalues has a Method option is easy, though:
>
> >     Options[Eigenvalues]
> > {Cubics -> False, Method -> Automatic, Quartics -> False}
>
> > What is difficult (impossible), however, is to find out for a Method
> > option -- and a number of functions have it -- is what the possible
> > settings are.
>
> ...
>
> Eigenvalues[HilbertMatrix[4],Method->"foo"]
> Eigenvalues::emeth: The method specified by Method -> foo should be
> either Automatic, Arnoldi, or BandedMatrix.
>
> works often, not always.

Michael,
This is the method I used in the past, plus some info from the ARPACK
documentation (since this is what the Arnoldi method ends up calling
internally). I've summarized the resulting documentation here:

http://groups.google.com/group/comp.soft-sys.math.mathematica/browse_thread/thread/2a41064c0dbe5d54/26f379d722f6e1c8?hl=en#26f379d722f6e1c8
Roman


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