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Diagonalizing large sparse matrices

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!


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