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The solution of the matrix equation AXB=D and the system of matrix equations AX=C,XB=D with X*X=Ip

Author

Listed:
  • Zhang, Huiting
  • Liu, Lina
  • Liu, Hao
  • Yuan, Yongxin

Abstract

In this paper, the solvability conditions for the matrix equation AXB=D and a pair of matrix equations AX=C,XB=D with the constraint X*X=Ip are deduced by applying the spectral and singular value decompositions of matrices, and the expressions of the general solutions to these matrix equations are also provided. Furthermore, the associated optimal approximate problems to the given matrices are discussed and the optimal approximate solutions are derived. Finally, two numerical experiments are given to validate the accuracy of the results.

Suggested Citation

  • Zhang, Huiting & Liu, Lina & Liu, Hao & Yuan, Yongxin, 2022. "The solution of the matrix equation AXB=D and the system of matrix equations AX=C,XB=D with X*X=Ip," Applied Mathematics and Computation, Elsevier, vol. 418(C).
    • Handle: RePEc:eee:apmaco:v:418:y:2022:i:c:s0096300321008717
    DOI: 10.1016/j.amc.2021.126789
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    References listed on IDEAS

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    1. Liu, Zhongyun & Li, Zhen & Ferreira, Carla & Zhang, Yulin, 2020. "Stationary splitting iterative methods for the matrix equation AXB=C," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    2. Yuan, Yongxin & Zuo, Kezheng, 2015. "The Re-nonnegative definite and Re-positive definite solutions to the matrix equation AXB=D," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 905-912.
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