The minimal norm least squares Hermitian solution of the complex matrix equation AXB+CXD=E
The minimal norm least squares Hermitian solution of the complex matrix equation AXB+CXD=E
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DOI：
10.1016/j.jfranklin.2017.12.023
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发表时间：
2018-02
期刊：
影响因子：
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通讯作者：
Fengxia Zhang;M. Wei;Ying Li;Jianli Zhao
中科院分区：
文献类型：
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作者：
Fengxia Zhang;M. Wei;Ying Li;Jianli Zhao
本文利用复矩阵的真实的表示、真实的表示的特殊结构和Moore-Penrose广义逆，得到了复矩阵方程A × B+ C × D= E的极小范数最小二乘Hermite解的显式表达式.并给出了复矩阵方程AX B= E的极小范数最小二乘Hermite解。我们提出的公式只涉及真实的矩阵，因此比Yuan和Liao（2014）中报道的公式更有效和更可移植。相应的算法只执行真实的运算，同时也考虑了复矩阵的真实的表示的特殊结构。两个数值例子证明了我们的算法的有效性。
In this paper, by applying the real representations of complex matrices, the particular structure of the real representations and the Moore–Penrose generalized inverse, we obtain the explicit expression of the minimal norm least squares Hermitian solution of the complex matrix equation A X B+ C X D= E. And we also derive the minimal norm least squares Hermitian solution of the complex matrix equation A X B= E. Our proposed formulas only involve real matrices, and therefore are more effective and portable than those reported in Yuan and Liao (2014). The corresponding algorithms only perform real arithmetic which also consider the particular structure of the real representations of complex matrices. Two numerical examples are provided to demonstrate the effectiveness of our algorithms.