Karim Belabas on Wed, 13 Nov 2013 11:38:03 +0100


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Re: Gram–Schmidt orthogonalization? 

* Dirk Laurie [2013-11-13 10:53]:
> 2013/11/13 Karim Belabas <Karim.Belabas@math.u-bordeaux1.fr>:
> 
> > We finally have matqr() since February 2013. :-)  (It uses Householder
> > reflections rather than Gram-Schmidt, but the end result is the same.)
> 
> Actually, the end result is better, in the sense that the
> computed basis satisfies sharper bounds on numerical
> deviation from orthogonality.

Indeed, that was my original motivation ( in the context of improving
our floating point LLL, before we scrapped everything to replace it by
Stehle's fplll :-).

I played a bit with Givens rotations as well at the time, but my
implementation was slower and not much stabler.

Cheers,

    K.B.
--
Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
Universite Bordeaux 1          Fax: (+33) (0)5 40 00 69 50
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