Algorithm 782: Codes for rank-revealing QR factorizations of dense matrices. 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 [cf. the authors paper, ibid. 24, No. 2, 226--253 (1998; reviewed above)]. The main contribution is an efficient block algorithm for approximating an RRQR factorization, employing a windowed version of the commonly used pivoting strategy proposed by {it G. Golub} [Numer. Math. 7, 206--216 (1965; Zbl 142.11502)] and improved versions of the RRQR algorithms for triangular matrices originally suggested by {it S. Chandrasekaran} and {it I. C. F. Ipsen} [SIAM J. Matrix Anal. Appl. 15, No. 2, 592--622 (1994; Zbl 796.65030)] and by {it C.-T. Pan} and {it P. T. P. Tang} [SVD and signal processing III, 157--165 (1995; Zbl 826.65032)], respectively. We highlight usage and features of these codes. (Source:

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 22 articles , 1 standard article )

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  1. Yuan, Cheng; Yang, Jerry Zhijian; Li, Xiantao: An effective and easy-to-implement boundary condition for molecular dynamics simulations (2019)
  2. Lee, Tsung-Lin; Li, Tien-Yien; Zeng, Zhonggang: RankRev: a Matlab package for computing the numerical rank and updating/downdating (2018)
  3. Drmač, Zlatko: Algorithm 977: A QR-preconditioned QR SVD method for computing the SVD with high accuracy (2017)
  4. Martinsson, Per-Gunnar; Quintana Ortí, Gregorio; Heavner, Nathan; van de Geijn, Robert: Householder QR factorization with randomization for column pivoting (HQRRP) (2017)
  5. Drmač, Zlatko; Gugercin, Serkan: A new selection operator for the discrete empirical interpolation method -- improved a priori error bound and extensions (2016)
  6. Benner, Peter; Losse, Philip; Mehrmann, Volker; Voigt, Matthias: Numerical linear algebra methods for linear differential-algebraic equations (2015)
  7. Benner, Peter; Kürschner, Patrick; Saak, Jens: Efficient handling of complex shift parameters in the low-rank Cholesky factor ADI method (2013)
  8. Fassino, Claudia; Torrente, Maria-Laura: Simple varieties for limited precision points (2013)
  9. Barbella, G.; Perotti, F.; Simoncini, V.: Block Krylov subspace methods for the computation of structural response to turbulent wind (2011)
  10. Mahoney, Michael W.: Randomized algorithms for matrices and data (2011)
  11. Baur, U.: Low rank solution of data-sparse Sylvester equations (2008)
  12. Baur, Ulrike: Control-oriented model reduction for parabolic systems. (2008)
  13. Drmač, Zlatko; Veselić, Krešimir: New fast and accurate Jacobi SVD algorithm. II (2008)
  14. Drmač, Zlatko; Veselić, Krešimir: New fast and accurate Jacobi SVD algorithm. I (2008)
  15. Gentle, James E.: Matrix algebra. Theory, computations, and applications in statistics (2007)
  16. Baur, U.; Benner, P.: Factorized solution of Lyapunov equations based on hierarchical matrix arithmetic (2006)
  17. Bandyopadhyay, A. K.; Tomassoni, C.; Mongiardo, M.; Omar, A. S.: Generalized multipole technique without redundant multipoles (2005)
  18. Hansen, Per Christian; Yalamov, Plamen Y.: Computing symmetric rank-revealing decompositions via triangular factorization (2001)
  19. Johansson, Lars: A Newton method for rigid body frictional impact with multiple simultaneous impact points (2001)
  20. Pan, C.-T.: On the existence and computation of rank-revealing LU factorizations (2000)

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