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On the parameterized two-step iteration method for solving the matrix equation AXB = C

Author

Listed:
  • Tian, Zhaolu
  • Wang, Yudong
  • Wu, Nian-Ci
  • Liu, Zhongyun

Abstract

In this paper, based on the iteration framework [10], by introducing two tuning parameters α,β in the splittings of the matrices A and B, a parameterized two-step iteration (PTSI) method is presented for solving the matrix equation AXB=C. In the sequel, the convergence property and choices of the parameters α,β are analyzed in detail. For some special cases of the matrices A and B, the corresponding PTSI methods are also investigated, and the optimal parameters α,β can be obtained for the symmetric positive definite (SPD) matrices A and B. In addition, some comparison results of the PTSI method are given for the M-matrices A,B compared with the TSI method [10]. Finally, several numerical examples are performed to verify the efficiencies of the PTSI method and choices of the optimal parameters.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:464:y:2024:i:c:s0096300323005702
    DOI: 10.1016/j.amc.2023.128401
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    References listed on IDEAS

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    1. 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).
    2. 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.
    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).
    4. 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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