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Linear and Multilinear Algebra Volume 71, 2023 - Issue 2
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Research Article

A randomised iterative method for solving factorised linear systems

Jing Zhaoa Department of Mathematics, School of Sciences, Nanchang University, Nanchang, Jiangxi, People's Republic of China;b School of Science, East China University of Technology, Nanchang, Jiangxi, People's Republic of ChinaView further author information
,
Xiang Wanga Department of Mathematics, School of Sciences, Nanchang University, Nanchang, Jiangxi, People's Republic of ChinaCorrespondence[email protected]
View further author information
&
Jianhua Zhangb School of Science, East China University of Technology, Nanchang, Jiangxi, People's Republic of ChinaView further author information
Pages 242-255 | Received 29 May 2020, Accepted 31 Oct 2021, Published online: 17 Jan 2022

References

  • Adomavicius G, Tuzhilin A. Toward the next generation of recommender systems: a survey of the state-of-the-art and possible extensions. IEEE Trans Knowl Data Eng. 2005;17:734–749.
  • Koren Y, Bell B, Volinsky C. Matrix factorization techniques for recommender systems. Computer. 2009;42:30–37.
  • Keshavan RH, Montanari A, Oh S. Matrix completion from noisy entries. J Mach Learn Res. 2010;11:2057–2078.
  • Koltchinskii V, Lounici K, Tsybakov AB. Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion. Ann Stat. 2011;39:2302–2329.
  • Verbert K, Manouselis N, Ochoa X, et al. Context-aware recommender systems for learning: a survey and future challenges. IEEE Trans Learn Technol. 2012;5:318–335.
  • Goes J, Zhang T, Arora R, et al. Robust stochastic principal component analysis. Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics, PMLR Reykjavik, Iceland. Vol. 33; 2014. p. 266–274.
  • Ma A, Needell D, Ramdas A. Iterative methods for solving factorized linear systems. SIAM J Matrix Anal Appl. 2018;39:104–122.
  • Strohmer T, Vershynin R. A randomized Kaczmarz algorithm with exponential convergence. J Fourier Anal Appl. 2009;15:262–278.
  • Leventhal D, Lewis AS. Randomized methods for linear constraints: convergence rates and conditioning. Math Oper Res. 2010;35:641–654.
  • Zouzias A, Freris NM. Randomized extended Kaczmarz for solving least squares. SIAM J Matrix Anal Appl. 2013;34:773–793.
  • Ma A, Needell D, Ramdas A. Convergence properties of the randomized extended Gauss–Seidel and Kaczmarz methods. SIAM J Matrix Anal Appl. 2015;36:1590–1604.
  • Needell D. Randomized Kaczmarz solver for noisy linear systems. BIT. 2010;50:395–403.
  • Dumitrescu B. On the relation between the randomized extended Kaczmarz algorithm and coordinate descent. BIT. 2014;55:1–11.
  • Ma A, Needell D, Ramdas A. Iterative methods for solving factorized linear systems. [cited 2019 Jan 9]. Available from: https://arxiv.org/abs/1701.07453
  • Du K. Tight upper bounds for the convergence of the randomized extended Kaczmarz and Gauss–Seidel algorithms. Numer Linear Algebra Appl. 2019;26:e2233.
  • Bai Z-Z, Wu W-T. On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM J Sci Comput. 2018;40:A592–A606.
  • Bai Z-Z, Wu W-T. On greedy randomized coordinate descent methods for solving large linear least-squares problems. Numer Linear Algebra Appl. 2019;26:e22371

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