数学理论与应用 ›› 2016, Vol. 36 ›› Issue (4): 23-28.

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约束矩阵方程的Hermitian解的共轭梯度迭代算法

岳潇荣, 周富照   

  1. 长沙理工大学数学与统计学院,长沙,410114
  • 出版日期:2016-12-30 发布日期:2020-09-25
  • 基金资助:
    国家自然科学基金资助项目(11371072)

A Conjugate Gradient Iterative Algorithm for Hermitian Solutions of Matrix Equations with Constraints

Yue Xiaorong, Zhou Fuzhao   

  1. School of Mathematics and Statistics,Changsha University of Science and Technology,Changsha 410014,China
  • Online:2016-12-30 Published:2020-09-25

摘要: 本文讨论矩阵方程在子矩阵约束下的Hermitian解的共轭梯度迭代算法,先转化成两个低阶方程,然后利用共轭梯度思想分别构造出低阶方程的共轭梯度迭代算法,运用算法求出矩阵方程的Hermitian解及最佳逼近,最后给出了数值实例来验证算法的有效性.

关键词: 子矩阵约束, Hermitian解, 共轭梯度迭代法, 最佳逼近解

Abstract:

In this paper,we give a conjugate gradient iterative algorithm for Hermitian solutions of matrix equations under submatrix constraints.First,we transform the equations into two lower-order equations,then we construct a gradient iterative algorithm by conjugate gradients for lower-order equations to obtain the solutions and the optimal approximation of the matrix equations.Finally some numerical examples are given to verify the effectiveness of this method.

Key words: Submatrix constraint, Hermitian solution, Conjugate gradient iterative, Optimal approximation