Efficient algorithms for computing the condition number of a tridagonal matrix
SIAM Journal on Scientific and Statistical Computing
SIAM Journal on Scientific and Statistical Computing
An aplicaiton of systolic arrays to linear discrete Ill posed problems
SIAM Journal on Scientific and Statistical Computing
A storage-efficient WY representation for products of householder transformations
SIAM Journal on Scientific and Statistical Computing
A block QR factorization algorithm using restricted pivoting
Proceedings of the 1989 ACM/IEEE conference on Supercomputing
SIAM Journal on Scientific and Statistical Computing
Incremental condition estimation
SIAM Journal on Matrix Analysis and Applications
Algorithm 686: FORTRAN subroutines for updating the QR decomposition
ACM Transactions on Mathematical Software (TOMS)
An updating algorithm for subspace tracking
An updating algorithm for subspace tracking
A parallel QR factorization algorithm with controlled local pivoting
SIAM Journal on Scientific and Statistical Computing
Structure-preserving and rank-revealing QR-factorizations
SIAM Journal on Scientific and Statistical Computing
LAPACK's user's guide
Some applications of the rank revealing QR factorization
SIAM Journal on Scientific and Statistical Computing
Determining rank in the presence of error
Determining rank in the presence of error
The modified truncated SVD method for regularization in general form
SIAM Journal on Scientific and Statistical Computing
On Rank-Revealing Factorisations
SIAM Journal on Matrix Analysis and Applications
Matrix computations (3rd ed.)
A BLAS-3 Version of the QR Factorization with Column Pivoting
SIAM Journal on Scientific Computing
Rank degeneracy and least squares problems
Rank degeneracy and least squares problems
LAPACK Working Note 33: Robust Incremental Condition Estimation
LAPACK Working Note 33: Robust Incremental Condition Estimation
Algorithm 782: codes for rank-revealing QR factorizations of dense matrices
ACM Transactions on Mathematical Software (TOMS)
Parallel Partial Stabilizing Algorithms for Large Linear Control Systems
The Journal of Supercomputing
Efficient Algorithms for the Block Hessenberg Form
The Journal of Supercomputing
New Parallel (Rank-Revealing) QR Factorization Algorithms
Euro-Par '02 Proceedings of the 8th International Euro-Par Conference on Parallel Processing
Partial stabilisation of large-scale discrete-time linear control systems
International Journal of Computational Science and Engineering
On the Failure of Rank-Revealing QR Factorization Software -- A Case Study
ACM Transactions on Mathematical Software (TOMS)
Unsupervised feature selection for principal components analysis
Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining
Clustered subset selection and its applications on it service metrics
Proceedings of the 17th ACM conference on Information and knowledge management
An improved approximation algorithm for the column subset selection problem
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Semiblind Multiuser MIMO Channel Estimators Using PM and RRQR Methods
CNSR '09 Proceedings of the 2009 Seventh Annual Communication Networks and Services Research Conference
ARMS - automatic residue-minimization based sampling for multi-point modeling techniques
Proceedings of the 46th Annual Design Automation Conference
RRQR based closed-form blind carrier offset estimator for OFDM systems
ICT'09 Proceedings of the 16th international conference on Telecommunications
High resolution joint time delay and frequency estimation
SARNOFF'09 Proceedings of the 32nd international conference on Sarnoff symposium
Journal of Computational Physics
3POr: parallel projection based parameterized order reduction for multi-dimensional linear models
Proceedings of the International Conference on Computer-Aided Design
Randomized Algorithms for Matrices and Data
Foundations and Trends® in Machine Learning
Simple varieties for limited precision points
Theoretical Computer Science
ACM Transactions on Mathematical Software (TOMS)
| Hi-index | 0.01 |
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.