Sparse solver for large symmetric matrices

I have available large sparse matrices from a FEM software (ANSYS) to use for an eigenvalue problem.

The problem is i can not store 10^6 x 10^6 sparse matrices in matlab because it is too big.

Did anybody experienced and solved similar problem?

ANsys allows to convert in harwell boeing format these matrices, which are sparse, but then i can't store inside matlab and use them for apply a banal eigen value problem using for example the routine "eigs".

Thanks for the help

[Matt J]

10^6 x 10^6 isn't a very large size for a sparse matrix. If it's not fitting in memory, it most likely means the number of non-zero entries is inappropriately large.

[Christine Tobler]

Can you say more about how you are loading this matrix into MATLAB, and how big the file you are trying to import is?

If you are able to export this sparse matrix as a simple list of triplets (row index, column index, value), or in matrix market format, this would probably be easier to import. All code for importing harwell-boeing matrices I found online seems to just be dead links to previously existing code.

Answer 1

[Andrew Knyazev]

both eigs and http://www.mathworks.com/matlabcentral/fileexchange/48-lobpcg-m can be used in a matrix-free fashion, only needing a function the performs the matrix-vector products that the user can provide.