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Stationary splitting iterative methods for the matrix equation AXB=C

Author

Listed:
  • Liu, Zhongyun
  • Li, Zhen
  • Ferreira, Carla
  • Zhang, Yulin

Abstract

Stationary splitting iterative methods for solving AXB=C are considered in this paper. The main tool to derive our new method is the induced splitting of a given nonsingular matrix A=M−N by a matrix H such that (I−H)−1 exists. Convergence properties of the proposed method are discussed and numerical experiments are presented to illustrate its computational efficiency and the effectiveness of some preconditioned variants. In particular, for certain surface fitting applications our method is much more efficient than the progressive iterative approximation (PIA), a conventional iterative method often used in computer aided geometric design (CAGD).

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:378:y:2020:i:c:s0096300320301648
    DOI: 10.1016/j.amc.2020.125195
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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.
    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.
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    Citations

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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. Zhang, Huiting & Liu, Lina & Liu, Hao & Yuan, Yongxin, 2022. "The solution of the matrix equation AXB=D and the system of matrix equations AX=C,XB=D with X*X=Ip," Applied Mathematics and Computation, Elsevier, vol. 418(C).
    3. Lili Xing & Wendi Bao & Weiguo Li, 2023. "On the Convergence of the Randomized Block Kaczmarz Algorithm for Solving a Matrix Equation," Mathematics, MDPI, vol. 11(21), pages 1-15, November.

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    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).
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