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A Gradient Based Iterative Solutions for Sylvester Tensor Equations

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  • Zhen Chen
  • Linzhang Lu

Abstract

This paper is concerned with the numerical solution of the Sylvester tensor equation, which includes the Sylvester matrix equation as special case. By applying hierarchical identification principle proposed by Ding and Chen, 2005, and by using tensor arithmetic concepts, an iterative algorithm and its modification are established to solve the Sylvester tensor equation. Convergence analysis indicates that the iterative solutions always converge to the exact solution for arbitrary initial value. Finally, some examples are provided to show that the proposed algorithms are effective.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnlmpe:819479
    DOI: 10.1155/2013/819479
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    Cited by:

    1. 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).
    2. 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).
    3. Tao Li & Qing-Wen Wang & Xin-Fang Zhang, 2022. "A Modified Conjugate Residual Method and Nearest Kronecker Product Preconditioner for the Generalized Coupled Sylvester Tensor Equations," Mathematics, MDPI, vol. 10(10), pages 1-19, May.
    4. Zhang, Xin-Fang & Wang, Qing-Wen, 2021. "Developing iterative algorithms to solve Sylvester tensor equations," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    5. Xiao, Lin & Li, Xiaopeng & Jia, Lei & Liu, Sai, 2022. "Improved finite-time solutions to time-varying Sylvester tensor equation via zeroing neural networks," Applied Mathematics and Computation, Elsevier, vol. 416(C).

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