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- To: eigen@xxxxxxxxxxxxxxxxxxx
- Subject: [eigen] Some background about LDLT
- From: hauke strasdat <strasdat@xxxxxxxxx>
- Date: Tue, 26 Jul 2011 12:21:19 +0100
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Hi,
I am using the LDLT method
(http://eigen.tuxfamily.org/dox/classEigen_1_1LDLT.html) on
semi-definite matrices quite heavily and it is working well for me.
However, I would like to learn some more about this very successful
approach. I wonder, is there any good reference (preferably an
academic paper) about it?
In particular, I would like to know:
- The LDLT method differs from standard Cholesky by two features:
* The diagonal D.
* The pivoting P'LDL'P.
Is it correct to say that D is added for speed and accuracy reasons
(avoid square root), while the pivoting is added to stabilise accuracy
for rank deficient matrices (with a minimal cost overhead)?
- Is it possible/practical to use LDLT without pivoting on
rank-deficient semi-definite matrices?
- What is the speed/accuracy table
(http://eigen.tuxfamily.org/dox/TutorialLinearAlgebra.html) based on.
Thanks a lot in advance,
Hauke S.