Re: QR vs. Gram Schmidt
- To: mathgroup at smc.vnet.net
- Subject: [mg20742] Re: QR vs. Gram Schmidt
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Wed, 10 Nov 1999 00:17:52 -0500
- Organization: Universitaet Leipzig
- References: <7vrbdh$2h8@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hi Greg,
I would like to see the QR decomposition of the vectors
{1,x,x^2,x^3, ...}
with InnerProduct[f_,g_]:=Integrate[f[x]*g[x] *Exp[-x],{x,0,Infinity}]
Regards
Jens
garnold wrote:
>
> Here's something interesting... QR & Gram Schmidt are fundamentally the same
> thing. They are exactly the same for a #rows>=#cols and trivially the same
> for #rows<#cols.
>
> So... why is GramSchmidt a separate package that must be loaded in? QR is
> MUCH faster at least in the Mathematica 4.0 implementation. Of course this
> is expected since QR is in the kernel.
>
> So... I have 2 related questions:
> (1) Is one algorithm theoretically faster than the other?
> (2) Does anybody have a good reference for understanding the QR algorithm
> when #rows > # cols? (Mathematica claims it uses Hausdorf transformations,
> but I don't understand this since Q is no longer square).
>
> Thanks!
>
> Greg