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 89 articles )

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  1. Cai, Jian-Feng; Wang, Tianming; Wei, Ke: Fast and provable algorithms for spectrally sparse signal reconstruction via low-rank Hankel matrix completion (2019)
  2. Del Corso, Gianna M.; Romani, Francesco: Adaptive nonnegative matrix factorization and measure comparisons for recommender systems (2019)
  3. Goldenberg, Steven; Stathopoulos, Andreas; Romero, Eloy: A Golub-Kahan Davidson method for accurately computing a few singular triplets of large sparse matrices (2019)
  4. Hu, Yunyi; Andersen, Martin S.; Nagy, James G.: Spectral computed tomography with linearization and preconditioning (2019)
  5. Jia, Zhigang; Ng, Michael K.; Song, Guang-Jing: Lanczos method for large-scale quaternion singular value decomposition (2019)
  6. Khamaru, Koulik; Mazumder, Rahul: Computation of the maximum likelihood estimator in low-rank factor analysis (2019)
  7. Long, Andrew W.; Ferguson, Andrew L.: Landmark diffusion maps (L-dMaps): accelerated manifold learning out-of-sample extension (2019)
  8. Ma, Feng: On relaxation of some customized proximal point algorithms for convex minimization: from variational inequality perspective (2019)
  9. Zeng, Xueying; Shen, Lixin; Xu, Yuesheng; Lu, Jian: Matrix completion via minimizing an approximate rank (2019)
  10. Alekseenko, Alexander; Nguyen, Truong; Wood, Aihua: A deterministic-stochastic method for computing the Boltzmann collision integral in (\mathcalO(MN)) operations (2018)
  11. Cai, Jian-Feng; Wang, Tianming; Wei, Ke: Spectral compressed sensing via projected gradient descent (2018)
  12. Fithian, William; Mazumder, Rahul: Flexible low-rank statistical modeling with missing data and side information (2018)
  13. He, Hongjin; Hou, Liusheng; Xu, Hong-Kun: A partially isochronous splitting algorithm for three-block separable convex minimization problems (2018)
  14. Niu, Datian; Meng, Jiana; Li, Hongying: A new shift strategy for the implicitly restarted refined harmonic Lanczos method (2018)
  15. Park, Dohyung; Kyrillidis, Anastasios; Caramanis, Constantine; Sanghavi, Sujay: Finding low-rank solutions via nonconvex matrix factorization, efficiently and provably (2018)
  16. Shabat, Gil; Shmueli, Yaniv; Aizenbud, Yariv; Averbuch, Amir: Randomized LU decomposition (2018)
  17. Gaaf, Sarah W.; Simoncini, Valeria: Approximating the leading singular triplets of a large matrix function (2017)
  18. Goldfarb, Donald; Mu, Cun; Wright, John; Zhou, Chaoxu: Using negative curvature in solving nonlinear programs (2017)
  19. Scott, Tony C.; Therani, Madhusudan; Wang, Xing M.: Data clustering with quantum mechanics (2017)
  20. Wen, Zaiwen; Zhang, Yin: Accelerating convergence by augmented Rayleigh-Ritz projections for large-scale eigenpair computation (2017)

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