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The least squares solution of a class of generalized Sylvester-transpose matrix equations with the norm inequality constraint

Author

Listed:
  • Baohua Huang

    (Fujian Normal University)

  • Changfeng Ma

    (Fujian Normal University)

Abstract

In this paper, we present an iterative method for finding the least squares solution of a class of generalized Sylvester-transpose matrix equations with the norm inequality constraint. We prove that if the constrained matrix equations are consistent, the solution can be obtained within finite iterative steps in the absence of round-off errors; if constrained matrix equations are inconsistent, the least squares solution can be obtained within finite iterative steps in the absence of round-off errors. Finally, numerical examples are provided to illustrate the efficiency of the proposed method and testify the conclusions suggested in this paper.

Suggested Citation

  • Baohua Huang & Changfeng Ma, 2019. "The least squares solution of a class of generalized Sylvester-transpose matrix equations with the norm inequality constraint," Journal of Global Optimization, Springer, vol. 73(1), pages 193-221, January.
    • Handle: RePEc:spr:jglopt:v:73:y:2019:i:1:d:10.1007_s10898-018-0692-4
    DOI: 10.1007/s10898-018-0692-4
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    References listed on IDEAS

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    1. Magnus, J.R., 1983. "L-structured matrices and linear matrix equations," Other publications TiSEM ef9a74f0-816a-4079-8211-1, Tilburg University, School of Economics and Management.
    2. Mehdi Dehghan & Masoud Hajarian, 2012. "The generalised Sylvester matrix equations over the generalised bisymmetric and skew-symmetric matrices," International Journal of Systems Science, Taylor & Francis Journals, vol. 43(8), pages 1580-1590.
    3. Aijing Liu & Guoliang Chen & Xiangyun Zhang, 2013. "A New Method for the Bisymmetric Minimum Norm Solution of the Consistent Matrix Equations ," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-6, March.
    4. Masoud Hajarian, 2016. "Least Squares Solution of the Linear Operator Equation," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 205-219, July.
    5. Jiao-fen Li & Wen Li & Ru Huang, 2016. "An efficient method for solving a matrix least squares problem over a matrix inequality constraint," Computational Optimization and Applications, Springer, vol. 63(2), pages 393-423, March.
    6. Xie, Ya-Jun & Ma, Chang-Feng, 2016. "The accelerated gradient based iterative algorithm for solving a class of generalized Sylvester-transpose matrix equation," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 1257-1269.
    7. Huang, Baohua & Ma, Changfeng, 2018. "An iterative algorithm for the least Frobenius norm least squares solution of a class of generalized coupled Sylvester-transpose linear matrix equations," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 58-74.
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