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 109 articles )

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  1. Bosner, Nela: Parallel Prony’s method with multivariate matrix pencil approach and its numerical aspects (2021)
  2. Jia, Zhongxiao; Li, Haibo: The joint bidiagonalization process with partial reorthogonalization (2021)
  3. Palitta, Davide; Kürschner, Patrick: On the convergence of Krylov methods with low-rank truncations (2021)
  4. Wang, Haifeng; Cai, Jian-Feng; Wang, Tianming; Wei, Ke: Fast Cadzow’s algorithm and a gradient variant (2021)
  5. Zeng, Chao; Ng, Michael K.: Incremental CP tensor decomposition by alternating minimization method (2021)
  6. Dax, Achiya: A cross-product approach for low-rank approximations of large matrices (2020)
  7. Gazzola, Silvia; Meng, Chang; Nagy, James G.: Krylov methods for low-rank regularization (2020)
  8. He, Bingsheng; Ma, Feng; Yuan, Xiaoming: Optimally linearizing the alternating direction method of multipliers for convex programming (2020)
  9. Lazzaro, Damiana; Morigi, Serena: Matrix completion for matrices with low-rank displacement (2020)
  10. Li, Huan; Lin, Zhouchen: Provable accelerated gradient method for nonconvex low rank optimization (2020)
  11. Mazumder, Rahul; Saldana, Diego; Weng, Haolei: Matrix completion with nonconvex regularization: spectral operators and scalable algorithms (2020)
  12. Mitchell, Tim: Computing the Kreiss constant of a matrix (2020)
  13. Polizzi, Eric; Saad, Yousef: Computational materials science and engineering (2020)
  14. Zhang, Liping; Wei, Yimin: Randomized core reduction for discrete ill-posed problem (2020)
  15. Alaya, Mokhtar Z.; Klopp, Olga: Collective matrix completion (2019)
  16. Cai, Jian-Feng; Wang, Tianming; Wei, Ke: Fast and provable algorithms for spectrally sparse signal reconstruction via low-rank Hankel matrix completion (2019)
  17. Dax, Achiya: Computing the smallest singular triplets of a large matrix (2019)
  18. Del Corso, Gianna M.; Romani, Francesco: Adaptive nonnegative matrix factorization and measure comparisons for recommender systems (2019)
  19. Feng, Yuehua; Xiao, Jianwei; Gu, Ming: Flip-flop spectrum-revealing QR factorization and its applications to singular value decomposition (2019)
  20. Goldenberg, Steven; Stathopoulos, Andreas; Romero, Eloy: A Golub-Kahan Davidson method for accurately computing a few singular triplets of large sparse matrices (2019)

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