       Re: eigenvector computations

• To: mathgroup at smc.vnet.net
• Subject: [mg117360] Re: eigenvector computations
• From: "Hans Michel" <hmichel at cox.net>
• Date: Wed, 16 Mar 2011 06:26:52 -0500 (EST)

```http://reference.wolfram.com/legacy/v5_2/Built-inFunctions/AdvancedDocumenta
tion/LinearAlgebra/LinearAlgebraInMathematica/MatrixComputations/Eigensystem

Under Legacy

>From Document Center in version 7

tutorial/LinearAlgebraMatrixComputations
under Obsolete

Scroll to "ARPACK".

-----Original Message-----
From: Bill Thurston [mailto:wpthurston at mac.com]
Sent: Tuesday, March 15, 2011 6:05 AM
To: mathgroup at smc.vnet.net
Subject: [mg117360] [mg117328] eigenvector computations

I'm doing some computations where I need to find the size of the leading
eigenvalue of various matrices that depend on a rational number between 0
and 1.  The matrices are mostly 0, with nonzero entries 1 or 2.  I'm doing
this using
sparse matrices and, for a matrix A,  asking for
First@Abs[ Eigenvalues[ N[ A],1]]
which usually works fine, but sometimes I get error messages like this:

Eigenvalues::maxit2 :  "Warning: maximum number of iterations, 1000, has
been \
reached by the Arnoldi algorithm without convergence to the specified \
tolerance, but the current best computed value has been returned. You can
use \
method options with Method -> {Arnoldi, opts} to increase the size of basis
\
vectors, the maximum number of iterations, reduce the tolerance, or use an \
estimate as a shift, any of which may help."

This would be fine except that I can't find any Mathematica documentation
for the Arnoldi method or its options.
What gives?
Bill Thurston

```

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