[ssawyer06]

Interesting, a direct sparse solver (for structured sparse matrices?). The name "clique" implies graph theory, so I was expecting to see distributed iterative SVD. I've yet to see a good distributed SVD for huge real-world/power-law graphs.

[poulson]

Sparse-direct solvers use graph theory to exploit nonzeros. In particular, Clique uses recursive nodal bisection ("nested dissection") for this purpose. The separators from this process end up (more-or-less) becoming cliques in the graph implied by the factored sparse matrix. Each of these cliques ends up corresponding to a dense matrix, which I then factor/solve-against using Elemental.

[knepley]

SLEPc, http://www.grycap.upv.es/slepc/, has distributed SVD for sparse matrices.

[poulson]

Yes, I should have mentioned this. SLEPc has the only distributed implementation of partial reorthogonalization (the key component of high-performance Krylov SVD and Hermitian eigensolvers) that I'm aware of.