Restarted block Lanczos bidiagonalization methods. The problem of computing a few of the largest or smallest singular values and associated singular vectors of a large matrix arises in many applications. This paper describes restarted block Lanczos bidiagonalization methods based on augmentation of Ritz vectors or harmonic Ritz vectors by block Krylov subspaces. (netlib numeralgo na26)

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  1. Francisco, J.B.; Viloche Bazán, F.S.; Weber Mendonça, M.: Non-monotone algorithm for minimization on arbitrary domains with applications to large-scale orthogonal Procrustes problem (2017)
  2. Wu, Lingfei; Stathopoulos, Andreas: A preconditioned hybrid SVD method for accurately computing singular triplets of large matrices (2015)
  3. Baglama, J.; Fenu, C.; Reichel, L.; Rodriguez, G.: Analysis of directed networks via partial singular value decomposition and Gauss quadrature (2014)
  4. Hearn, Tristan A.; Reichel, Lothar: Fast computation of convolution operations via low-rank approximation (2014)
  5. Niu, Datian; Yuan, Xuegang: An implicitly restarted Lanczos bidiagonalization method with refined harmonic shifts for computing smallest singular triplets (2014)
  6. Baglama, James; Reichel, Lothar: An implicitly restarted block Lanczos bidiagonalization method using Leja shifts (2013)
  7. Baglama, J.; Reichel, L.; Richmond, D.: An augmented LSQR method (2013)
  8. Hochstenbach, Michiel E.: Probabilistic upper bounds for the matrix two-norm (2013)
  9. Martin, David R.; Reichel, Lothar: Projected Tikhonov regularization of large-scale discrete ill-posed problems (2013)
  10. Tzeng, Jengnan: Split-and-combine singular value decomposition for large-scale matrix (2013)
  11. Niu, Datian; Yuan, Xuegang: A harmonic Lanczos bidiagonalization method for computing interior singular triplets of large matrices (2012)
  12. Morgan, Ronald B.; Nicely, Dywayne A.: Restarting the nonsymmetric Lanczos algorithm for eigenvalues and linear equations including multiple right-hand sides (2011)
  13. Jia, Zhongxiao; Niu, Datian: A refined harmonic Lanczos bidiagonalization method and an implicitly restarted algorithm for computing the smallest singular triplets of large matrices (2010)
  14. Baglama, James: Augmented block Householder Arnoldi method (2008)
  15. Guidotti, Patrick; Lambers, James V.: Eigenvalue characterization and computation for the Laplacian on general 2-D domains (2008)
  16. Baglama, James; Reichel, Lothar: Restarted block Lanczos bidiagonalization methods (2006)