[eigen] Re: LU partial pivoting: LUP versus PLU |

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*To*: eigen@xxxxxxxxxxxxxxxxxxx*Subject*: [eigen] Re: LU partial pivoting: LUP versus PLU*From*: Benoit Jacob <jacob.benoit.1@xxxxxxxxx>*Date*: Wed, 28 Jan 2009 22:32:53 +0100*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=PW47ZOTdHzSISpcOh/Fkrp66bkixg1jeKQtsE24PvXg=; b=MS2goGfzssvlvqm0p4W3qnG8lecuLaLjKM3+lKyTJOzQapV/OyvInJxqj5B0WbP/W0 sG8w/ObIIGK0FHQju1uscKCOZXJrDL2yIqagIxvbdZZ5qfCvg1FXeQO5RUFT2bTio50G oyur9iCl5KP/M4kr6I9KGJ3T7U3WzIb+hva7A=*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=sfq7ZaIIh9wPfYSwUx6mHjzRAFqmlqqa8BeB2BPJWALDxqZ51LOqhissYtI+Ny5Kwb BVQP/09xq/z3/AqkelPAYbyApCWce+HXkojvC2KoOM8x35TiW0vzjDOi7nvv5f3srOAG gztmWDqp8WHjzcXwyuxyREz/MlNEx/EjjsHsw=

OK, last email. IF it really matters, we can still get partial pivoting working for all (rows,cols) combinations, by actually permuting both rows and columns. There is a small price for that, but it would be quite low and still far less expensive than full pivoting because the pivot lookup would stay the same as in plain partial pivoting. But what I was wondering is that perhaps it doesn't matter at all... Also the case rows>=cols probably doesn't matter for LU because in that case (overconstrained) people will want to do least squares anyway....? This would be an argument in favor of LUP which has the two other benefits that 1) it's closest in notation to full pivoting (PLUQ) and 2) it's closest to what we do by hand when we solve systems by Gaussian elimination. Benoit 2009/1/28 Benoit Jacob <jacob.benoit.1@xxxxxxxxx>: > 2009/1/28 Benoit Jacob <jacob.benoit.1@xxxxxxxxx>: >> my U matrix must have all the nonzero diagonal coefficients grouped at >> the beginning. > > Let me rephrase that: my matrix U must have all the "leading > coefficients" lying on the main diagonal. > > Here I call "leading coefficient" any coefficient that is the first > nonzero coefficient in its own row (going from left to right). > > Cheers, > Benoit >

**References**:**[eigen] LU partial pivoting: LUP versus PLU***From:*Benoit Jacob

**[eigen] Re: LU partial pivoting: LUP versus PLU***From:*Benoit Jacob

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