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Algorithm 782: codes for rank-revealing QR factorizations of dense matrices
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Source ACM Transactions on Mathematical Software (TOMS) archive
Volume 24 ,  Issue 2  (June 1998) table of contents
Pages: 254 - 257  
Year of Publication: 1998
ISSN:0098-3500
Authors
C. H. Bischof  Argonne National Lab, Argonne, IL
G. Quintana-Ortí  Univ. Jaime I, Castellón, Spain
Publisher
ACM  New York, NY, USA
Bibliometrics
Downloads (6 Weeks): 4,   Downloads (12 Months): 84,   Citation Count: 3
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appendices and supplements   abstract   references   cited by   index terms   review   collaborative colleagues  

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APPENDICES and SUPPLEMENTS
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Software for "Computing Rank-Revealing QR Factorizations of Dense Matrices"


ABSTRACT

This article describes a suite of codes as well as associated testing and timing drivers for computing rank-revealing QR (RRQR) factorizations of dense matrices. The main contribution is an efficient block algorithm for approximating an RRQR factorization, employing a windowed version of the commonly used Golub pivoting strategy and improved versions of the RRQR algorithms for triangular matrices orginally suggersted by Chandrasekaran and Ipsen and by Pan and Tang, respectively, We highlight usage and features of these codes.


REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

 
1
E. Anderson , Z. Bai , C. Bischof , J. Demmel , J. Dongarra , J. Du Croz , A. Greenbaum , S. Hammarling , A. McKenney , S. Ostrouchov , D. Sorensen, LAPACK's user's guide, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1992
2
Christian H. Bischof , G. Quintana-Ortí, Computing rank-revealing QR factorizations of dense matrices, ACM Transactions on Mathematical Software (TOMS), v.24 n.2, p.226-253, June 1998  [doi>10.1145/290200.287637]
 
3
Shivkumar Chandrasekaran , Ilse C. F. Ipsen, On Rank-Revealing Factorisations, SIAM Journal on Matrix Analysis and Applications, v.15 n.2, p.592-622, April 1994  [doi>10.1137/S0895479891223781]
 
4
PAN, C.-T. AND TANG, P. T. P. 1992. Bounds on singular values revealed by QR factorization. Tech. Rep. MCS-P332-1092. Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL.

CITED BY  3
Leslie Foster , Rajesh Kommu, Algorithm 853: An efficient algorithm for solving rank-deficient least squares problems, ACM Transactions on Mathematical Software (TOMS), v.32 n.1, p.157-165, March 2006
Christos Boutsidis , Jimeng Sun , Nikos Anerousis, Clustered subset selection and its applications on it service metrics, Proceeding of the 17th ACM conference on Information and knowledge management, October 26-30, 2008, Napa Valley, California, USA
Christos Boutsidis , Michael W. Mahoney , Petros Drineas, Unsupervised feature selection for principal components analysis, Proceeding of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining, August 24-27, 2008, Las Vegas, Nevada, USA

INDEX TERMS

Primary Classification:
  D. Software
  D.3 PROGRAMMING LANGUAGES
      D.3.2 Language Classifications

          Nouns: FORTRAN 77

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS


General Terms:
Algorithms, Performance


Keywords:
block algorithm, numerical rank, rank-revealing QR factorization


REVIEW

"Charles Raymond Crawford : Reviewer"

A rank-revealing QR (RRQR) factorization is an efficient way to compute a reasonable representation of the null space of a matrix. This paper and the accompanying algorithm describe and analyze a suite of codes that implement combi  more...

Collaborative Colleagues:
C. H. Bischof: colleagues
G. Quintana-Ortí: colleagues

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