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Re: Eigenvalues Okay, Eigenvectors Fail

  • To: mathgroup at smc.vnet.net
  • Subject: [mg88742] Re: Eigenvalues Okay, Eigenvectors Fail
  • From: jfuite at phys.ualberta.ca
  • Date: Thu, 15 May 2008 06:52:34 -0400 (EDT)
  • References: <fupm4m$s4r$1@smc.vnet.net>

Okay, a week later, I can answer my own question for the benefit of
someone else someday, perhaps.

To recap, I had a large (n = 733), square (n x n), real matrix, mSub,
and asked why, if I could find eigenvalues in short order, my computer
could not find the eigenvectors?  Such that,
A. Timing@Eigenvalues[mSub] = {2 Second, l}, where l is a list of
eigenvalues of length n, but,
B. Eigenvectors[mSub] does not complete.

Anyway, I still do not completely understand what is happening, but I
get the sense that Mathematica was simply not converging to an answer
quickly with the default settings for the function Eigenvectors.
Reading Trott, "Mathematica Guidebook for Numerics", chapter 1.4, and
later Mathematica Help, "Advanced Documentation - Linear Algebra", I
learned of some obscure options for the function Eigenvectors, and set
up the following function which runs quickly and provides the kind of
answers I need:

Eigensystem[mSub, 4, Method->{"Arnoldi", Criteria->"BothEnds",
MaxIterations->10^3, Tolerance->10^-3}]



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