Re: [eigen] Fast QR for 2x2, 3x3

[Benoit Jacob <jacob.benoit.1@xxxxxxxxx>]

Hi,

It would be very useful to have fixed-size specializations of QR for
2x2 and 3x3. You're very welcome to help us with that, and for that
matter you can submit us the code in any format, it'll be easy to
integrate in Eigen.

I can't tell what's going to be faster, Givens or Householder or
something else. All I can say for sure is that Givens rotations don't
require computing cosines and sines!

Here you can find a copy of Golub & van Loan: download.tuxfamily.org/eigen

Cheers,
Benoit


2009/2/22 Andrea Arteaga <yo.eres@xxxxxxxxx>:
> Hi.
> I'm Andrea Arteaga and I'm student of Computing Science and Engeneering at
> ETH
> Zurich.
> I read this in the todo-page
> (http://eigen.tuxfamily.org/index.php?title=Todo#QR_module):
>
> implement efficient QR decomposition for 2x2 and 3x3 matrix with optional
> computation of R (maybe using Gram-Schmitd instead of Householder
> transformations ?)
>
> I thought that Givens Rotations
> (http://en.wikipedia.org/wiki/Givens_rotation) are perfect for that: the
> computation of a givens-matrix requires only (execution of sin()) +
> (execution of cos()) operations; the product between two 2x2 matrices
> requires only 8 operations and maybe less than that.
> If you need it, I can help a little bit, QR is one of my preferred topics!
>
> [I'm sorry for my bad english, I live in Switzerland and I never studied
> well english...]
>
>