Hi Umut,
one of the reasons is the parallelism: When doing Householder
reflections, you can only process one reflection at a time without any
good data reuse. 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.
Best regards,
Karli
On 07/15/2013 03:42 PM, Umut Tabak wrote:
On 07/15/2013 08:54 PM, Matthew Knepley wrote:
On Jul 15, 2013 1:51 PM, "Umut Tabak" <[email protected]
<mailto:[email protected]>> wrote:
>
> Hi list,
>
> I was wondering the reason why classical gram schmidt is used in the
orthogonalizations in the gmres implementation as default? As far as I
remember, this was unstable numerically.
Hi Matt,
Excuse my naive question but mathematically they are equivalent so what
is the source of speed boost? And can you please direct me to one or two
of these references?
Best,
Umut
Its much faster. Try the modified option and compare. There are many
papers claiming that classical+selective reorthogonalization is just
as stable.
Matt
>
> Best,
> Umut
