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The Jacobi and Gauss–Seidel-type iteration methods for the matrix equation AXB=C

Author

Listed:
  • Tian, Zhaolu
  • Tian, Maoyi
  • Liu, Zhongyun
  • Xu, Tongyang

Abstract

In this paper, the Jacobi and Gauss–Seidel-type iteration methods are proposed for solving the matrix equation AXB=C, which are based on the splitting schemes of the matrices A and B. The convergence and computational cost of these iteration methods are discussed. Furthermore, we give the preconditioned Jacobi and Gauss–Seidel-type iteration methods. Numerical examples are given to demonstrate the efficiency of these methods proposed in this paper.

Suggested Citation

  • Tian, Zhaolu & Tian, Maoyi & Liu, Zhongyun & Xu, Tongyang, 2017. "The Jacobi and Gauss–Seidel-type iteration methods for the matrix equation AXB=C," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 63-75.
    • Handle: RePEc:eee:apmaco:v:292:y:2017:i:c:p:63-75
    DOI: 10.1016/j.amc.2016.07.026
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    Cited by:

    1. Tian, Zhaolu & Wang, Yudong & Wu, Nian-Ci & Liu, Zhongyun, 2024. "On the parameterized two-step iteration method for solving the matrix equation AXB = C," Applied Mathematics and Computation, Elsevier, vol. 464(C).
    2. Tian, Zhaolu & Li, Xiaojing & Dong, Yinghui & Liu, Zhongyun, 2021. "Some relaxed iteration methods for solving matrix equation AXB=C," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    3. Liu, Zhongyun & Zhou, Yang & Zhang, Yuelan & Lin, Lu & Xie, Dongxiu, 2019. "Some remarks on Jacobi and Gauss–Seidel-type iteration methods for the matrix equation AXB=C," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 305-307.
    4. Liu, Zhongyun & Li, Zhen & Ferreira, Carla & Zhang, Yulin, 2020. "Stationary splitting iterative methods for the matrix equation AXB=C," Applied Mathematics and Computation, Elsevier, vol. 378(C).

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