Singular value and generalized singular value decompositions and the solution of linear matrix equations
Singular value and generalized singular value decompositions and the solution of linear matrix equations
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DOI：
10.1016/0024-3795(87)90104-2
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发表时间：
1987-04
影响因子：
1.1
通讯作者：
K. Chu
中科院分区：
文献类型：
--
作者：
K. Chu
本文考虑线性矩阵方程（i）AXB+CYD= E和（ii）（AXB，FXG）=（E，H）的解。新的必要条件和充分条件的一致性的方程推导，一些使用广义奇异值分解。特殊情况（iii）AX+YD= E和（iv）AXB= E用奇异值分解处理。并给出了求解的数值算法。
The solution of the linear matrix equations (i)AXB+CYD=Eand (ii) (AXB,FXG)=(E,H) are considered. New necessary and sufficient conditions for the consistency of the equations are derived, some using the generalized singular value decomposition. Special cases (iii)AX+YD=Eand (iv)AXB=Eare treated using the singular value decomposition. Numerical algorithms for the solutions are also suggested.