Re: [eigen] Re: LU precision tuning |

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*To*: eigen@xxxxxxxxxxxxxxxxxxx*Subject*: Re: [eigen] Re: LU precision tuning*From*: Benoit Jacob <jacob.benoit.1@xxxxxxxxx>*Date*: Mon, 11 May 2009 17:20:40 +0200*Dkim-signature*: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:mime-version:received:in-reply-to:references :date:message-id:subject:from:to:content-type :content-transfer-encoding; bh=ikWdjiAAUrWmsotStXK8rPVOV7R8sKN0Chs/NvJ1gtg=; b=Z9lKfzr4N1uzt86CFnHWk3iFrcp4srszxS4ofZcd4g/Jdk3YEQ+jMgN/T6FreR7K+n a8MSAx3srfoGuIUgWesNVVyGixwSXPx1WCGssklv4zsse/wiq7NSWFEW65J4lNQiwQ65 3dhMK/qVFDb/ABO5i6IUyDzo20uim4mQZ8UXU=*Domainkey-signature*: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=mime-version:in-reply-to:references:date:message-id:subject:from:to :content-type:content-transfer-encoding; b=XiFg+xW2MSmtD/qwa+K02AC5XIks4xzXgRuZEp97sWszEj39rR8jkkMhtY4HcnvAQp pKt3otOgr8gB66ARLTBSQI2aY4owa//NrHzfqV6mUgTqSEoer5GL4u+MdBVV3yux45Jw +I7PSj+KlFVvrJ0kcN3pMiBP4GY3KZ5M7apiE=

Ah, very interesting. A class named QR should guarantee Q square but it would be interesting to have ThinQR alongside. Cheers, Benoit 2009/5/11, Márton Danóczy <marton78@xxxxxxxxx>: >> 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 > > >

**References**:**[eigen] LU precision tuning***From:*Benoit Jacob

**Re: [eigen] Re: LU precision tuning***From:*Hauke Heibel

**Re: [eigen] Re: LU precision tuning***From:*Benoit Jacob

**Re: [eigen] Re: LU precision tuning***From:*Hauke Heibel

**Re: [eigen] Re: LU precision tuning***From:*Benoit Jacob

**Re: [eigen] Re: LU precision tuning***From:*Benoit Jacob

**Re: [eigen] Re: LU precision tuning***From:*Benoit Jacob

**Re: [eigen] Re: LU precision tuning***From:*Hauke Heibel

**Re: [eigen] Re: LU precision tuning***From:*Benoit Jacob

**Re: [eigen] Re: LU precision tuning***From:*Márton Danóczy

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