Re: [eigen] request for comments / help

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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.


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