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From: Jens Seidel (jensseidel_at_[hidden])
Date: 2007-12-23 16:05:36

On Sun, Dec 23, 2007 at 02:37:43PM +0200, Dima Sorkin wrote:
> Quoting Karl Meerbergen <karl.meerbergen_at_[hidden]>:
> > More expensive than QR but more reliable.
> > Jens Seidel wrote:
> > > Please note that some QR decompositions (especially if Gram Schmidt
> > > orthogonalisation is used) are very unstable and could cause trouble with
> > > small systems as 5x5 (at least if you expect a high accuracy)!!!!
> But when I have matrices of full rank (= min(M,N) where (N,M) are the sizes of
> the matrix), (with "reasonable" condition number), are these methods (QR and
> LQ) good enough ?

I never used the QR decomposition for larger problems but only to
improve interpolation rules in my own Algebraic Multigrid code by enforcing
linear interpolation which resulted in 4xN systems with N<20.

I learned that it is a bad idea to implement your own methods if you can
use proper designed and tested libraries.

> Otherwise why LAPACK's driver routine DGELS uses them ... (?)

I'm sure is uses more stable algorithms. Whether it works for your large
systems needs to be tested ...