Re: [Gretl-users] QR versus Cholesky decomposition
On Thu, July 20, 2006 17:35, Talha Yalta wrote:
Professor Cottrell:
During my testing of gretl using the StRD linear regressions test
suit, I found that QR decomposition performs better than the Cholesky
decomposition and sent you a pdf file containing a table comparing the
two methods. QR method mostly creates higher number of accurate digits
and is able to produce a solution for the Flip data set, where
Cholesky fails.
In the light of this evidence I wrote my paper and prepared the
summary tables assuming the new default for linear regressions would
be the QR decomposition. I see that the new snapshots still have
Cholesky as the default. If Cholesky will stay as the default in the
new version, please let me know so that I can update my tables.
I am attaching the pdf file containing the comparisons.
IIRC, Sven brought this up some time ago. I did a little testing, and QR is
about 10-15% slower than Cholesky. This is the price you have to pay for
greater accuracy. So, it all boils down to choosing speed over precision. I
would go for QR myself, but in 99.99% of the cases the difference in precision
is not even noticeable: the test cases you give are artificial datasets
especially designed to be very ill-conditioned (but, to be honest, I did
stumble once into a real-life dataset where Cholesky couldn't cut it and QR
would). Besides, with the CPUs we have today, a few microseconds are nothing.
What's other people's opinion?
Riccardo "Jack" Lucchetti
Dipartimento di Economia
Facoltà di Economia "G. Fuà"
Ancona