[petsc-dev] Scalability of removing null spaces

[Jed Brown]

On Sun, Jul 22, 2012 at 1:50 PM, Matthew Knepley <knepley at gmail.com> 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).
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