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