### Rank Revealing QR factorization (RRQR)

Posted:

**Tue May 24, 2011 1:42 am**
by **vvvnsk**

Long time ago in 1986 I made my student thesis on RRQR, where had developed algorithm on how to make it efficiently and correctly. After that, I switched to work on various projects not connected with the subject. Recently, I recall that work in context of page rank calculation and found that so far it looks like no final solution developed for RRQR. So I am wondering if there is any interest in that problem (I guess it is) and what to do with my results? Any advice from this community?

Thanks!

### Re: Rank Revealing QR factorization (RRQR)

Posted:

**Mon Feb 06, 2012 6:05 am**
by **akobotov**

Hello Vladimir,

There is indeed some interest in this. And even an implementation is already developed in LAPACK style (

http://www.netlib.org/toms/782), which follows article “Computing Rank-Revealing QR Factorizations of Dense Matrices”.

To LAPACKers,

I'm also curious if there any plans to include the functionality? Or there are some reasons not to include it? It is still out of the package being available since 1998...

Thanks,

Alexander.

### Re: Rank Revealing QR factorization (RRQR)

Posted:

**Mon Feb 06, 2012 6:53 am**
by **Julien Langou**

Hello Alex and Vladimir,

The LAPACK algorithm for pivoted QR using Level 3 BLAS is DGEQP3. TOMS #782 compares with DGEQPF which is less efficient than DGEQP3.

(I think DGEQP3 was included in LAPACK after TOMS#782, and is largely based on it, Gregorio is actually a common co-author of the DGEQP3

subroutines and of TOM#782.) We can reinvestigate all this. One of the main issues here is that it is not clear how much efficient these

algorithms are in the light of multicore architectures,

Cheers,

Julien.