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Conjugate gradient least squares algorithm for solving the generalized coupled Sylvester-conjugate matrix equations

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  • Hu, Jingjing
  • Ma, Changfeng

Abstract

In this study, we consider the minimum-norm least squares solution of the generalized coupled Sylvester-conjugate matrix equations by conjugate gradient least squares algorithm. When the system is consistent, the exact solution can be obtained. When the system is inconsistent, the least squares solution can be obtained within finite iterative steps in the absence of round-off error for any initial matrices. Furthermore, we can get the minimum-norm least squares solution by choosing special types of initial matrices. Finally, some numerical examples are given to demonstrate the algorithm considered is quite effective in actual computation.

Suggested Citation

  • Hu, Jingjing & Ma, Changfeng, 2018. "Conjugate gradient least squares algorithm for solving the generalized coupled Sylvester-conjugate matrix equations," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 174-191.
    • Handle: RePEc:eee:apmaco:v:334:y:2018:i:c:p:174-191
    DOI: 10.1016/j.amc.2018.03.119
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    References listed on IDEAS

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    1. 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.
    2. 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.
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