Least squares Hermitian solution of the matrix equation (AXB, CXD) = (E, F) with the least norm over the skew field of quaternions

Least squares Hermitian solution of the matrix equation (AXB, CXD) = (E, F) with the least norm over the skew field of quaternions
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DOI：
10.1016/j.mcm.2007.08.009
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发表时间：
2008-07
期刊：
Math. Comput. Model.
影响因子：
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通讯作者：
Shifang Yuan;A. Liao;Yuan Lei
Shifang Yuan;A. Liao;Yuan Lei
中科院分区：
其他
文献类型：
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作者：
Shifang Yuan;A. Liao;Yuan Lei

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利用四元数矩阵的复表示、Moore-Penrose广义逆和矩阵的Kronecker积，导出了四元数体上具有最小范数的矩阵方程（AXB，CXD）=（E，F）的最小二乘Hermite解的表达式，并给出了计算上述解的数值算法.
By using the complex representations of quaternion matrices, Moore–Penrose generalized inverse and the Kronecker product of matrices, we derive the expression of the least squares Hermitian solution of the matrix equation (AXB,CXD)=(E,F) with the least norm over the skew field of quaternions, and provide a numerical algorithm to calculate the forementioned solution.