On Wed, Apr 25, 2012 at 19:46, Mark F. Adams <[email protected]>wrote:

I think we shouldn't try to encode the near-null space being sparse. For elasticity, we would only reduce the 18 matrix entries to 12, which is only about break-even on storage since the dense null space can use fewer column indices (this is ignoring the dense case also being more efficient).

Its worse than that in aggregation MG, I think, because P is not the null space but Q in a QR decomposition of the rigid body modes ... that might still have some sparsity, not sure.

Well, the translational modes are position-independent, so they should retain sparsity with a standard implementation of QR (in the sense that the zeros will remain very close to 0 so that you could discard them, though I don't think it's even worth trying to do that).