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Re: Behavior of Eigenvalues and Eigensystem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg115099] Re: Behavior of Eigenvalues and Eigensystem
  • From: Michael Weyrauch <michael.weyrauch at gmx.de>
  • Date: Thu, 30 Dec 2010 19:05:58 -0500 (EST)
  • References: <ifhib3$i3v$1@smc.vnet.net>

Hello,

the command should be


  Eigensystem[{mat1,mat2},3, Method ->  Arnoldi]

with brackets aound the two matrices for a generalized eigenvalue
problem.

But you are right, this command is badly documented and we
had a recent discussion about this on this group. There were
a few elements of information on various settings related to the Arnoldi
method discussed in that thread, e.g.

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


I also noticed that for some strange reason Mathematica
adds an unnessary imaginary part like 0.I to the second matrix (even
if you give purly real matrices) and then complains that
the matrix is not positive definite.

My first attempts to calculate generalized eigenvalues using the
Arnoldi Method inside Mathematice also failed. If there is
a workaround I do not know yet, I need to investigate that
soon. Maybe somebody else has some more useful information.

Michael



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