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Re: Diagonalizing large sparse matrices



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


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