QR vs. Gram Schmidt
- To: mathgroup at smc.vnet.net
- Subject: [mg20619] QR vs. Gram Schmidt
- From: "garnold" <garnold at mbvlab.wpafb.af.mil>
- Date: Thu, 4 Nov 1999 02:13:33 -0500
- Sender: owner-wri-mathgroup at wolfram.com
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