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A Modified Conjugate Residual Method and Nearest Kronecker Product Preconditioner for the Generalized Coupled Sylvester Tensor Equations

Author

Listed:
  • Tao Li

    (Department of Mathematics, Key Laboratory of Engineering Modeling and Statistical Computation of Hainan Province, Hainan University, Haikou 570228, China)

  • Qing-Wen Wang

    (Department of Mathematics, Shanghai University, Shanghai 200444, China
    Collaborative Innovation Center for the Marine Artificial Intelligence, Shanghai 200444, China)

  • Xin-Fang Zhang

    (Department of Mathematics, Key Laboratory of Engineering Modeling and Statistical Computation of Hainan Province, Hainan University, Haikou 570228, China)

Abstract

This paper is devoted to proposing a modified conjugate residual method for solving the generalized coupled Sylvester tensor equations. To further improve its convergence rate, we derive a preconditioned modified conjugate residual method based on the Kronecker product approximations for solving the tensor equations. A theoretical analysis shows that the proposed method converges to an exact solution for any initial tensor at most finite steps in the absence round-off errors. Compared with a modified conjugate gradient method, the obtained numerical results illustrate that our methods perform much better in terms of the number of iteration steps and computing time.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1730-:d:818560
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    References listed on IDEAS

    as
    1. 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.
    2. 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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    Cited by:

    1. Long-Sheng Liu & Qing-Wen Wang & Mahmoud Saad Mehany, 2022. "A Sylvester-Type Matrix Equation over the Hamilton Quaternions with an Application," Mathematics, MDPI, vol. 10(10), pages 1-20, May.

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