Barry Smith <[email protected]> writes:

...

Actually, the problem is more subtle because if one wants an SPD multigrid cycle, they only need that the post-smoother is the transpose of the pre-smoother.

Hmm. Is this true? This guy’s matrix causes grief with indefiniteness but since it uses SSOR smoother I think that post-smooth should have been the transpose of the pre smooth automatically?

Yes, S_pre = S_post = S is symmetric so S_pre^T = S_post trivially. But S appears to be indefinite. It's simpler to understand indefiniteness for symmetric matrices (like SSOR), but we shouldn't get overzealous and put in checks for whether S is SPD.