MathGroup Archive 1999

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QR vs. Gram Schmidt

  • To: mathgroup at
  • Subject: [mg20619] QR vs. Gram Schmidt
  • From: "garnold" <garnold at>
  • Date: Thu, 4 Nov 1999 02:13:33 -0500
  • Sender: owner-wri-mathgroup at

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).



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