四元数矩阵方程的最小二乘解(英文)

The Least-Square Solutions to the Quaternion Matrix Equation Systems

利用四元数矩阵的广义奇异值分解,给出了下列四元数矩阵方程问题‖AXB-M‖2F+‖CXD-N‖2F=min解的一般表达式.

In this paper, the following problem is considered:Given A∈Q^(m×n), B∈Q^(p×q), M∈Q^(m×q), C∈Q^(l×n), D∈Q^(p×t), N∈Q^(l×t), find X∈Q^(n×p) such that‖AXB-M ‖~2_F+‖CXD-N‖~2_F=minBy applying the generalized singular value decomposition of quaternion matrices, the general solutions of above problem are obtained.