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From: Ted Dunning <ted.dunning@gmail.com>
Subject: Re: Is Cholesky too sensitive to rank deficiency?
Date: Mon, 17 Mar 2014 13:39:50 -0700
To: "dev@mahout.apache.org" <dev@mahout.apache.org>


This may not be an issue that can actually be cured. The cholesky trick is a=
kin to squaring a number.  Inherently you tend to lose precision by doing th=
is. =20

With the possibility of iteration we should consider more advanced methods f=
or large qr. The great value of the cholesky trick is that one can use map r=
educe with no iteration. =20

Sent from my iPhone

> On Mar 17, 2014, at 11:31, Dmitriy Lyubimov <dlieu.7@gmail.com> wrote:
>=20
> I still seem to get signficant differences on the norm differences of
> Householder QR and QR via Cholesky trick. our stock in-core QR seems to be=

> comfortable populating some R values (and therefore Q columns) with values=

> as small as 1e-16, whereas Cholesky computation for L seems to set these
> things to 0. Norms on Q in this case differ more than trivially.
>=20
> Are we sure we cannot decrease sensitivity of Cholesky decomposition to
> small values? I have manipulated the limit there that controls the decisio=
n
> for positive-definite-ness but I am not sure i understand algorithm well
> enough to do a meaningful sensitivity reduction.