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MathGroup Archive 2004

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Re: Eigensystem: different solution in V5.0 and V4.1 ??

  • To: mathgroup at smc.vnet.net
  • Subject: [mg48309] Re: Eigensystem: different solution in V5.0 and V4.1 ??
  • From: "Fred Klingener" <gigabitbucket at brockeng.com>
  • Date: Sun, 23 May 2004 06:15:36 -0400 (EDT)
  • References: <c8mu5a$8nu$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

"Ivo bleylevens" <ivo.bleylevens at facburfdaw.unimaas.nl> wrote in message
news:c8mu5a$8nu$1 at smc.vnet.net...
> Hello all !
>
> I am a dutch PhD student at the University of Maastricht and I have a
> question about some strange behaviour of the Mathematica's 5.0
> function Eigensystem[]. I have an 512x512 non-symmetric complex matrix
> M. When i use the command eigsys = Eigensystem[M] in Mathematica 5.0,
> the eigenvalues were not the eigenvalues I expected ! I calculated
> exactly the same notebook in Mathematica version 4.1 and these
> eigenvalues look the same as the wanted eigenvalues !! Am i doing
> something wrong in version 5.0 ??
>
> * I already tried to use the options of Eigensystem[] described at
>
http://documents.wolfram.com/v5/Built-inFunctions/AdvancedDocumentation/LinearAlgebra/4.4.html
> but that also didn't help.
>
> * I tried to set the precision of Mathematica 5.0 with the command
> eigsys = Eigensystem[N[M, 30]] but that didn't help either !
>
> * I also calculated the eigenvalues of the matrix M with another system
using
> the functions EIG and EIGS (which makes use op the LAPACK functions.
> Mathematica 5 uses this functions also as described in the link
> above). The eigenvalues computed with this two functions are exactly
> similar with the eigenvalues calculated in Mathematica 4.1....
>
> So in my opinion Mathematica 5.0 produces incorrect
> eigenvalues......can someone help me ???

Eigensolvers are notorious for producing "wrong" solutions, but very often
correct results are presented in forms or combinations that are not
immediately recognizable.  For example, one solver can produce eigenvectors
that are linear combinations of those produced by another, all valid
solutions.

Your first task should be to verify that the solution produced by 5.0 is
truly incorrect.  Plug your results back into the fundamental relationship.

Hth,
Fred Klingener


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