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

Author

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  • Liu, Zhongyun
  • Zhou, Yang
  • Zhang, Yuelan
  • Lin, Lu
  • Xie, Dongxiu

Abstract

Tian, et al. proposed in [5] several Jacobi and Gauss–Seidel-type iterative methods for solving matrix equation AXB=C. Those methods were demonstrated to be effective by the given numerical experiments. However, we find that there is a technical error in the proof of the main theorem (Theorem 3.3). In this note we first show this erratum by an example. Then we establish a new convergence theorem which contains the Theorem 3.3 in [5] as a special case.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:354:y:2019:i:c:p:305-307
    DOI: 10.1016/j.amc.2019.02.014
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    References listed on IDEAS

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    1. 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.
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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. 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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    2. 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).
    3. 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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