Re: Diagonalizing large sparse matrices
- To: mathgroup at smc.vnet.net
- Subject: [mg116484] Re: Diagonalizing large sparse matrices
- From: Oliver Ruebenkoenig <ruebenko at wolfram.com>
- Date: Wed, 16 Feb 2011 06:45:34 -0500 (EST)
Hello Mikhail,
On Wed, 16 Feb 2011, Mikhail Lemeshko wrote:
> Dear friends,
>
> Are there any ways to speed up the Eigenvalues[] problem for large
> sparse matrices (those I have are about 15000x15000)?
>
> I need only the first eigenvalue (which is usually negative), here is
> the code fragment:
>
> e0=Parallelize[-Eigenvalues[N[matr], 1, Method -> {Arnoldi, Criteria -
>> RealPart}]]
>
> (I have a 2 core processor)
>
> Many thanks in advance!
>
> Misha
>
>
Parallelize will be of no use here - the parallelization happens inside the
Eigenvalues. Try something like
m = 15000;
s = SparseArray[{{i_, i_} -> -2., {i_, j_} /; Abs[i - j] == 1 ->
1.}, {m, m}];
(*s=SparseArray[N[matr]]*)
Eigenvalues[s, 1, Method -> {Arnoldi}]
Oliver