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Re: eigenvector computations

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  • Subject: [mg117381] Re: eigenvector computations
  • From: Peter Pein <petsie at>
  • Date: Wed, 16 Mar 2011 06:30:45 -0500 (EST)
  • References: <ilnh6k$o8e$>

Am 15.03.2011 12:05, schrieb Bill Thurston:
> 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

Hi Bill,

sometimes Mathematica tells you at least the names of some options:

Eigenvalues[{{1}}, Method -> {"Arnoldi", "foo" -> "bar"}];
Eigenvalues::moptx:Method option foo in {Arnoldi,foo->bar} is not one of 
{Shift,Tolerance,BasisSize,MaxIterations,Criteria,StartingVector}. >>

But it is often not easy to guess valid values :-(

maybe this helps a bit,

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