On Sun, Jul 22, 2012 at 1:50 PM, Matthew Knepley <[email protected]> wrote:

I think we have to figure out how to do this pipelined thing in a mechanical way (not necessarily automated, but done without thinking). You would think this had been figured out by the architecture guys.

Bah, those guys don't use mathematical invariants so when they see an instruction sequence like a Krylov method, they say there is a data dependency and the pipeline stalls. The pipelined Krylov methods use the structure and the choices you make affect stability. In the case of GMRES, I think we just add an extra VecMDotBegin/End pair in with projection against the prior Krylov space (before normalization).