| Re: [eigen] request for comments / help |
[ Thread Index |
Date Index
| More lists.tuxfamily.org/eigen Archives
]
On 06/11/2012 06:31:22 PM, Gael Guennebaud wrote:
On Mon, Jun 11, 2012 at 5:56 PM, Helmut Jarausch
<jarausch@xxxxxxxxxxxxxxxxxxx> wrote:
> I've attached the corrected version of QR_Cholesky.
> Is it impudent to suggest adding this to Eigen?
>
> I think it's the standard way of solving the minimum length least
squares
> problem.
I think it would be better to perform a full orthogonalization of the
form:
A * P = Q * U * Z
where U of the form:
| U11 0 |
| 0 0 |
This can be done by applying householder reflexions on the non zero
upper trapezoidal part of the matrix R.
I have been using that myself - more than 20 years ago.
Recent references, like Peter Deuflhard's book on
Numerical Methods of Nonlinear Problems, Springer 2004,
recommendsthe use of QR-Cholesky (section 4.4.1).
Since Peter Deuflhard and his group have a lot of experience in
real life problems I am sure this suggestion has proven itself in
practise.
But if someone has an implementation of full orthogonalization we could
do
some benchmarking.
Helmut.