[petsc-users] default orthogonalization in gmres

Umut Tabak u.tabak at tudelft.nl
Mon Jul 15 17:38:00 CDT 2013

On 07/15/2013 11:57 PM, Jed Brown wrote:
> 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.
Dear Jed,

Could you please explain a bit more on what you mean by

+ reduction
+ normalization can be hidden

On a problem that I am working on, cgs and mgs have a subtle difference. 
I would like to learn more about these details.

More specifically, I would like to A orthonormalize a block of vectors, 
say for a block size of 4, however I can not form A explicitly because 
then it becomes large and dense. But it can be formed by a matrix vector 
operation. Due this reason, cgs and mgs is a little different for me, 
this is the source of the discussion.


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