Re: eigenvector computations
- To: mathgroup at smc.vnet.net
- Subject: [mg117381] Re: eigenvector computations
- From: Peter Pein <petsie at dordos.net>
- Date: Wed, 16 Mar 2011 06:30:45 -0500 (EST)
- References: <ilnh6k$o8e$1@smc.vnet.net>
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,
Peter