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Preconditioned BiCGSTAB and BiCRSTAB methods for solving the Sylvester tensor equation

Author

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  • Chen, Qi-Xing
  • Huang, Guang-Xin
  • Zhang, Ming-Yue

Abstract

This paper presents a biconjugate gradient stabilized (BiCGSTAB) method and a biconjugate residual stabilized (BiCRSTAB) method for solving the Sylvester tensor equation, respectively. Preconditioned BiCGSTAB and BiCRSTAB algorithms are also developed to solve the Sylvester tensor equation. The convergence of each proposed iterative algorithm is proved. Several numerical examples are shown to illustrate the effectiveness of the proposed methods.

Suggested Citation

  • Chen, Qi-Xing & Huang, Guang-Xin & Zhang, Ming-Yue, 2024. "Preconditioned BiCGSTAB and BiCRSTAB methods for solving the Sylvester tensor equation," Applied Mathematics and Computation, Elsevier, vol. 466(C).
    • Handle: RePEc:eee:apmaco:v:466:y:2024:i:c:s0096300323006380
    DOI: 10.1016/j.amc.2023.128469
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    References listed on IDEAS

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    1. Zhang, Xin-Fang & Wang, Qing-Wen, 2021. "Developing iterative algorithms to solve Sylvester tensor equations," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    2. Huang, Guang-Xin & Chen, Qi-Xing & Yin, Feng, 2022. "Preconditioned TBiCOR and TCORS algorithms for solving the Sylvester tensor equation," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    3. Zhen Chen & Linzhang Lu, 2013. "A Gradient Based Iterative Solutions for Sylvester Tensor Equations," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-7, March.
    4. Lv, Changqing & Ma, Changfeng, 2020. "A modified CG algorithm for solving generalized coupled Sylvester tensor equations," Applied Mathematics and Computation, Elsevier, vol. 365(C).
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