[petsc-users] default orthogonalization in gmres

[Karl Rupp]

Hey,

 >> However, for Gram-Schmidt you can just compute all the
>> necessary scalar products at the same time (VecMDot) and reuse the
>> common data vector. This gives you a speed-up of a factor of almost two.
>
> It's not a factor of 2, it's a factor of k where k is the size of the
> subspace.  Classical Gram-Schmidt needs one reduction per iteration
> (normalization can be hidden), but modified needs k reductions.

well, you see the factor of k only if the communication for the 
reduction is the bottleneck. The factor of almost 2 is what you get if 
memory bandwidth is the bottleneck.

Best regards,
Karli