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On the error estimate of the randomized double block Kaczmarz method

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  • Chen, Jia-Qi
  • Huang, Zheng-Da

Abstract

In this paper, we consider the convergence analysis of the randomized double block Kaczmarz method and improve the upper bound of the error estimate in expectation of the randomized double block Kaczmarz method. Numerical experiments are given to demonstrate the theoretical results and to show a large gap between the new and the old bound.

Suggested Citation

  • Chen, Jia-Qi & Huang, Zheng-Da, 2020. "On the error estimate of the randomized double block Kaczmarz method," Applied Mathematics and Computation, Elsevier, vol. 370(C).
    • Handle: RePEc:eee:apmaco:v:370:y:2020:i:c:s0096300319308999
    DOI: 10.1016/j.amc.2019.124907
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    References listed on IDEAS

    as
    1. Popa, Constantin & Zdunek, Rafal, 2004. "Kaczmarz extended algorithm for tomographic image reconstruction from limited-data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 65(6), pages 579-598.
    2. D. Leventhal & A. S. Lewis, 2010. "Randomized Methods for Linear Constraints: Convergence Rates and Conditioning," Mathematics of Operations Research, INFORMS, vol. 35(3), pages 641-654, August.
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    Cited by:

    1. Zhang, Yanjun & Li, Hanyu, 2021. "A count sketch maximal weighted residual Kaczmarz method for solving highly overdetermined linear systems," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    2. Du, Kui & Sun, Xiao-Hui, 2021. "A doubly stochastic block Gauss–Seidel algorithm for solving linear equations," Applied Mathematics and Computation, Elsevier, vol. 408(C).

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