[eigen] Some background about LDLT

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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.

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