Iterative algorithms for the generalized centro‐symmetric and central anti‐symmetric solutions of general coupled matrix equations
Iterative algorithms for the generalized centro‐symmetric and central anti‐symmetric solutions of general coupled matrix equations
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DOI：
10.1108/02644401211235870
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发表时间：
2012-07
影响因子：
1.6
通讯作者：
M. Dehghan;M. Hajarian
中科院分区：
文献类型：
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作者：
M. Dehghan;M. Hajarian
目的 – 本文的目的是找到两种迭代方法来求解广义中心对称和中心反对称矩阵上的一般耦合矩阵方程。设计/方法/途径 – 通过扩展共轭梯度 (CG) 方法的思想，作者提出了两种迭代方法来求解广义中心对称和中心反对称矩阵上的一般耦合矩阵方程。发现 – 当一般耦合矩阵方程在广义中心对称和中心反对称矩阵上一致时反对称矩阵，广义中心对称和中心反对称解可以在有限的迭代步骤内获得。最小弗罗贝尼乌斯范数广义中心对称和中心反对称解可以通过选择一种特殊的初始矩阵来导出。此外，给定广义中心对称和中心反对称的最优近似广义中心对称和中心反对称解......
Purpose – The purpose of this paper is to find two iterative methods to solve the general coupled matrix equations over the generalized centro‐symmetric and central antisymmetric matrices.Design/methodology/approach – By extending the idea of conjugate gradient (CG) method, the authors present two iterative methods to solve the general coupled matrix equations over the generalized centro‐symmetric and central antisymmetric matrices.Findings – When the general coupled matrix equations are consistent over the generalized centro‐symmetric and central anti‐symmetric matrices, the generalized centro‐symmetric and central anti‐symmetric solutions can be obtained within nite iterative steps. Also the least Frobenius norm generalized centrosymmetric and central anti‐symmetric solutions can be derived by choosing a special kind of initial matrices. Furthermore, the optimal approximation generalized centrosymmetric and central anti‐symmetric solutions to given generalized centro‐symmetric and central anti‐symmetric...