中心对称矩阵的广义中心对称{1, 4}逆的迭代算法
Iterative Algorithm for Generalized Centrosymmetric {1, 4} Inverse of Centrosymmetric Matrix
摘要:
广义逆在矩阵理论分析中有着重要的作用。文中讨论了中心对称矩阵A的广义中心对称{1, 4}逆的一种迭代算法，首先将广义{1, 4}逆转化为单变量线性矩阵方程组，然后建立求线性矩阵方阵组中心对称{1, 4}逆的修正共轭梯度算法(MCG算法)，证明了MCG算法的收敛性。数值算例表明，该算法具有很高的计算效率。
Abstract:
Generalized inverses play an important role in the analysis of matrix theory. In this paper, an iterative algorithm for generalized centrosymmetric {1, 4} inverse of centrosymmetric matrix is discussed. Firstly, the generalized {1, 4} inverse is transformed into a system of univariate linear matrix equations. Then, a modified conjugate gradient algorithm (MCG algorithm) is established for solving centrosymmetric {1, 4} inverses of linear matrices. The convergence of MCG algorithm is proved. Numerical examples show that the algorithm has high computational efficiency.
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