Computing rank-revealing QR factorizations of dense matrices.
We develop algorithms and implementations for computing rank-revealing QR (RRQR) factorizations of dense matrices. First, we develop an efficient block algorithm for approximating an RRQR factorization, employing a windowed version of the commonly used Golub pivoting strategy, aided by incremental condition estimation. Second, we develop efficiently implementable variants of guaranteed reliable RRQR algorithms for triangular matrices originally suggested by Chandrasekaran and Ipsen and by Pan and Tang. We suggest algorithmic improvements with respect to condition estimation, termination criteria, and Givens updating. By combining the block algorithm with one of the triangular postprocessing steps, we arrive at an efficient and reliable algorithm for computing an RRQR factorization of a dense matrix. Experimental results on IBM RS/6000 SGI R8000 platforms show that this approach performs up to three times faster that the less reliable QR factorization with column pivoting as it is currently implemented in LAPACK, and comes within 15% of the performance of the LAPACK block algorithm for computing a QR factorization without any column exchanges. Thus, we expect this routine to be useful in may circumstances where numerical rank deficiency cannot be ruled out, but currently has been ignored because of the computational cost of dealing with it.
- Research Organization:
- Argonne National Laboratory (ANL)
- Sponsoring Organization:
- ER
- DOE Contract Number:
- AC02-06CH11357
- OSTI ID:
- 937863
- Report Number(s):
- MCS-P559-0196
- Journal Information:
- ACM Trans. Math. Software, Journal Name: ACM Trans. Math. Software Journal Issue: 2 ; Jun. 1998 Vol. 24
- Country of Publication:
- United States
- Language:
- ENGLISH
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