An iterative algorithm for the reflexive solutions of the generalized coupled Sylvester matrix equations and its optimal approximation
An iterative algorithm for the reflexive solutions of the generalized coupled Sylvester matrix equations and its optimal approximation
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DOI：
10.1016/j.amc.2008.02.035
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发表时间：
2008-08
期刊：
影响因子：
--
通讯作者：
M. Dehghan;M. Hajarian
中科院分区：
文献类型：
--
作者：
M. Dehghan;M. Hajarian
具有未知矩阵Y，Z的广义耦合西尔维斯特矩阵方程（AY-ZB，CY-ZD）=（E，F）在许多系统和控制应用中会遇到。此外，这些矩阵方程有几个应用程序有关的问题，计算稳定的特征分解矩阵束。本文构造了求解自反矩阵Y，Z上广义耦合西尔维斯特矩阵方程的迭代算法。当矩阵方程组相容时，对任意初始矩阵对[Y 0，Z 0]，在无舍入误差的情况下，可在有限步迭代内得到一个自反解对，并通过选择一种特殊的初始矩阵对，可得到最小Frobenius范数自反解对.并得到了广义耦合西尔维斯特矩阵方程（AY-ZB，CY-ZD）=（E，F）的自反解对集中给定矩阵对[Y，Z]的最佳逼近自反解对.最后，通过数值算例验证了所提迭代算法的有效性.
The generalized coupled Sylvester matrix equations (AY-ZB,CY-ZD)=(E,F) with unknown matrices Y,Z are encountered in many systems and control applications. Also these matrix equations have several applications relating to the problem of computing stable eigendecompositions of matrix pencils. In this work, we construct an iterative algorithm to solve the generalized coupled Sylvester matrix equations over reflexive matrices Y,Z. And when the matrix equations are consistent, for any initial matrix pair [Y0,Z0], a reflexive solution pair can be obtained within finite iteration steps in the absence of roundoff errors, and the least Frobenius norm reflexive solution pair can be obtained by choosing a special kind of initial matrix pair. Also we obtain the optimal approximation reflexive solution pair to a given matrix pair [Y¯,Z¯] in the reflexive solution pair set of the generalized coupled Sylvester matrix equations (AY-ZB,CY-ZD)=(E,F). Moreover, several numerical examples are given to show the efficiency of the presented iterative algorithm.