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 100 articles )

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  1. Dax, Achiya: A cross-product approach for low-rank approximations of large matrices (2020)
  2. He, Bingsheng; Ma, Feng; Yuan, Xiaoming: Optimally linearizing the alternating direction method of multipliers for convex programming (2020)
  3. Lazzaro, Damiana; Morigi, Serena: Matrix completion for matrices with low-rank displacement (2020)
  4. Li, Huan; Lin, Zhouchen: Provable accelerated gradient method for nonconvex low rank optimization (2020)
  5. Mazumder, Rahul; Saldana, Diego; Weng, Haolei: Matrix completion with nonconvex regularization: spectral operators and scalable algorithms (2020)
  6. Polizzi, Eric; Saad, Yousef: Computational materials science and engineering (2020)
  7. Zhang, Liping; Wei, Yimin: Randomized core reduction for discrete ill-posed problem (2020)
  8. Alaya, Mokhtar Z.; Klopp, Olga: Collective matrix completion (2019)
  9. Cai, Jian-Feng; Wang, Tianming; Wei, Ke: Fast and provable algorithms for spectrally sparse signal reconstruction via low-rank Hankel matrix completion (2019)
  10. Dax, Achiya: Computing the smallest singular triplets of a large matrix (2019)
  11. Del Corso, Gianna M.; Romani, Francesco: Adaptive nonnegative matrix factorization and measure comparisons for recommender systems (2019)
  12. Feng, Yuehua; Xiao, Jianwei; Gu, Ming: Flip-flop spectrum-revealing QR factorization and its applications to singular value decomposition (2019)
  13. Goldenberg, Steven; Stathopoulos, Andreas; Romero, Eloy: A Golub-Kahan Davidson method for accurately computing a few singular triplets of large sparse matrices (2019)
  14. Hu, Yunyi; Andersen, Martin S.; Nagy, James G.: Spectral computed tomography with linearization and preconditioning (2019)
  15. Jia, Zhigang; Ng, Michael K.; Song, Guang-Jing: Lanczos method for large-scale quaternion singular value decomposition (2019)
  16. Khamaru, Koulik; Mazumder, Rahul: Computation of the maximum likelihood estimator in low-rank factor analysis (2019)
  17. Long, Andrew W.; Ferguson, Andrew L.: Landmark diffusion maps (L-dMaps): accelerated manifold learning out-of-sample extension (2019)
  18. Ma, Feng: On relaxation of some customized proximal point algorithms for convex minimization: from variational inequality perspective (2019)
  19. Zeng, Xueying; Shen, Lixin; Xu, Yuesheng; Lu, Jian: Matrix completion via minimizing an approximate rank (2019)
  20. Alekseenko, Alexander; Nguyen, Truong; Wood, Aihua: A deterministic-stochastic method for computing the Boltzmann collision integral in (\mathcalO(MN)) operations (2018)

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