Re: eigenvalues from dot-product

[David Bateman]

Daniel Oberhoff wrote:
> Ah, yes, I saw it now. Thank you. I used eigs before, but I didn't see
> that I could pass a function. It is still difficult as the storage
> requirement is O(k^2), i.e. O(1e9) bytes for my problem, since I need
> most of the eigenvalues. Using halve might already help though. Is
> there a way to further reduce memory requirements?
>
Without seeing the function you use for the matrix-vector multiplication
I can't really tell. I presume your function makes use of the symmetry
to reduce the number of operations. In fact I can't see a reason why the
matrix vector product routine would need any more memory than that
needed to store the matrix, input and output vectors. As for eigs
itself, it allocates working space based on the number of eigenvalues
you request. You can reduce the amount of memory allocated with the
opts.p value, though that might affect convergence... Finally it its the
memory allocation in eigs that is the problem, you might you several
separate calls to eigs to calculate the eigenvalues in groups, this will
be less efficient but will address the memory issue.

D.


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