The software package PROPACK contains a set of functions for computing the singular value decomposition of large and sparse or structured matrices. The SVD routines are based on the Lanczos bidiagonalization algorithm with partial reorthogonalization (BPRO). The Lanczos routines can also be used directly, and form the basis of efficient algorithms for solving linear systems of equations and linear least squares problems, in particular for systems with multiple right-hand sides.

References in zbMATH (referenced in 74 articles )

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  1. Niu, Datian; Meng, Jiana; Li, Hongying: A new shift strategy for the implicitly restarted refined harmonic Lanczos method (2018)
  2. Shabat, Gil; Shmueli, Yaniv; Aizenbud, Yariv; Averbuch, Amir: Randomized LU decomposition (2018)
  3. Gaaf, Sarah W.; Simoncini, Valeria: Approximating the leading singular triplets of a large matrix function (2017)
  4. Goldfarb, Donald; Mu, Cun; Wright, John; Zhou, Chaoxu: Using negative curvature in solving nonlinear programs (2017)
  5. Scott, Tony C.; Therani, Madhusudan; Wang, Xing M.: Data clustering with quantum mechanics (2017)
  6. Wen, Zaiwen; Zhang, Yin: Accelerating convergence by augmented Rayleigh-Ritz projections for large-scale eigenpair computation (2017)
  7. Wu, Lingfei; Romero, Eloy; Stathopoulos, Andreas: PRIMME_SVDS: a high-performance preconditioned SVD solver for accurate large-scale computations (2017)
  8. Cui, Li; Liu, Lu; Chen, Di-Rong; Xie, Jian-Feng: Recovery of low rank symmetric matrices via schatten $p$ norm minimization (2016)
  9. Friedlander, Michael P.; Mac^edo, Ives: Low-rank spectral optimization via gauge duality (2016)
  10. He, Hongjin; Han, Deren: A distributed Douglas-Rachford splitting method for multi-block convex minimization problems (2016)
  11. Hou, Liusheng; He, Hongjin; Yang, Junfeng: A partially parallel splitting method for multiple-block separable convex programming with applications to robust PCA (2016)
  12. Jin, Zheng-Fen; Wan, Zhongping; Jiao, Yuling; Lu, Xiliang: An alternating direction method with continuation for nonconvex low rank minimization (2016)
  13. Mikhalev, A.Yu.; Oseledets, I.V.: Iterative representing set selection for nested cross approximation. (2016)
  14. Mu, Cun; Zhang, Yuqian; Wright, John; Goldfarb, Donald: Scalable robust matrix recovery: Frank-Wolfe meets proximal methods (2016)
  15. Sorensen, D.C.; Embree, Mark: A DEIM induced CUR factorization (2016)
  16. Yang, Lei; Huang, Zheng-Hai; Hu, Shenglong; Han, Jiye: An iterative algorithm for third-order tensor multi-rank minimization (2016)
  17. Zhou, Yunkai; Wang, Zheng; Zhou, Aihui: Accelerating large partial EVD/SVD calculations by filtered block Davidson methods (2016)
  18. Aybat, N.S.; Iyengar, G.: An alternating direction method with increasing penalty for stable principal component pursuit (2015)
  19. Chung, Julianne; Knepper, Sarah; Nagy, James G.: Large-scale inverse problems in imaging (2015)
  20. Chung, Julianne; Palmer, Katrina: A hybrid LSMR algorithm for large-scale Tikhonov regularization (2015)

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