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- To: eigen@xxxxxxxxxxxxxxxxxxx
- Subject: Re: [eigen] Re: LU precision tuning
- From: Márton Danóczy <marton78@xxxxxxxxx>
- Date: Mon, 11 May 2009 17:18:09 +0200
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> Aha, the misunderstanding comes from an error in our current QR.
>
> Normally, in the QR decomposition, Q is always square, it's R that
> adapts to the rectangular size.
> http://en.wikipedia.org/wiki/QR_decomposition#Rectangular_matrix
>
> But here in our QR, it's Q that adapts to the rectangular size.
>
> Another problem --> so i wouldn't currently consider it reliable for
> non-square matrices.
Not necessarily. There's two versions of QR, in MATLAB's
implementation it's qr(A) or qr(A,0), where the second is called
"economy-size" QR, or "thin QR" by Golub & van Loan, see the wikipedia
page. The second is useful when looking for the least-squares solution
of overdetermined equations, i.e. when A is m x n and m>n. In this
case, using a full size Q (m x m) is a waste of memory, it's better to
have Q m x n and R n x n. If A is square or m<n, however, Q should be
m x m and R m x n.
Marton