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    $\begingroup$ Is the method Maindonald describes related to or the same as Gentleman's algorithm? jstor.org/stable/2347147 $\endgroup$ Commented Feb 5, 2011 at 21:46
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    $\begingroup$ In that case see also the extensions by Alan Miller jstor.org/stable/2347583. An archive of his Fortran software site is now at jblevins.org/mirror/amiller $\endgroup$ Commented Feb 5, 2011 at 22:44
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    $\begingroup$ An explicit algorithm appears at the bottom of p. 4 of saba.kntu.ac.ir/eecd/people/aliyari/NN%20%20files/rls.pdf . This can be found by Googling "recursive least squares." It does not look like an improvement on the Gentleman/Maindonald approach, but at least it is clearly and explicitly described. $\endgroup$ Commented Feb 5, 2011 at 23:20
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    $\begingroup$ The last link looks like the method I was going to suggest. The matrix identity they use is known in other places as the Sherman--Morrison--Woodbury identity. It is also quite numerically efficient to implement, but may not be as stable as a Givens rotation. $\endgroup$ Commented Feb 6, 2011 at 0:28
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    $\begingroup$ @suncoolsu Hmm... Maindonald's book was newly published when I started using it :-). $\endgroup$ Commented Feb 8, 2011 at 6:02