Gilles, Is the test checked in? I am interested in looking at it.
Thank you, -Greg On Thu, Sep 8, 2011 at 2:51 PM, Ted Dunning <ted.dunn...@gmail.com> wrote: > On Thu, Sep 8, 2011 at 12:42 PM, Luc Maisonobe <luc.maison...@free.fr > >wrote: > > > ... Luc - are there other reasons that QR would be better for cov > >> matrices? I would have to play with a bunch of examples, but I > >> suspect with the defaults, Cholesky may do the best job detecting > >> singular problems. > >> > > > > I'm not sure about Cholesky, but I have always thought that at least QR > was > > better than LU for near singular matrices, with only a factor 2 overhead > in > > number of operations (but number of operations is not the main bottleneck > in > > modern computers, cache behavior is more important). > > > This is my impression as well. > > In addition, Cholesky very nearly is a QR decomposition through the back > door. That is, if > > Q R = A > > Then > > R' R = A' A > > is the Cholesky decomposition. The algorithms are quite similar when > viewed > this way. Cholesky does not produce as accurate a result for R if you are > given A, but if you are given A'A as in the discussion here, it is pretty > much just as good, I think. > > I use this property for very large SVD's via stochastic projection because > Q > is much larger than R in that context so computing just R can be done > in-core while the full QR would require out-of-core operations. >
