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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2015, Vol. 32 ›› Issue (3): 397-415.doi: 10.3969/j.issn.1005-3085.2015.03.009

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一类矩阵方程组带有子矩阵约束的最小二乘中心对称解

彭卓华,   刘金旺   

  1. 湖南科技大学数学与计算科学学院，湘潭 411201
  • 收稿日期:2013-12-23 接受日期:2014-10-09 出版日期:2015-06-15 发布日期:2015-08-15
  • 基金资助:
    国家自然科学基金 (11471108)；湖南省高校创新平台开放基金 (13K087).

The Centro-symmetric Least Squares Solutions to a Class of Matrix Equations with a Submatrix Constraint

PENG Zhuo-hua,   LIU Jin-wang   

  1. School of Mathematics and Computing Science, Hunan University of Science and Technology, Xiangtan 411201
  • Received:2013-12-23 Accepted:2014-10-09 Online:2015-06-15 Published:2015-08-15
  • Supported by:
    The National Natural Science Foundation of China (11471108); the Open Foundation for the Innovation Platform of Universities in Hunan Province (13K087).

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摘要： 约束矩阵方程问题在控制理论、振动理论、工程和科学计算等领域具有重要应用．基于共轭梯度法的思想，本文构造了一种算法，以寻求一类矩阵方程组的带有子矩阵约束的最小二乘中心对称解．在没有舍入误差的情况下，该算法经过有限步迭代得到了矩阵方程组带子矩阵约束的最小二乘中心对称解，而且，通过选择一种特殊的初始矩阵，得到了矩阵方程组的带子矩阵约束的最小范数最小二乘中心对称解．数值实验显示该算法具有较快的收敛速度．

关键词: 中心主子矩阵, 中心对称解, 子矩阵约束, 最小二乘解, 最小范数解

Abstract:

The constrained matrix equation problem has a wide range of applications in control theory, vibration theory, engineering and science computing. In this paper, an algorithm is constructed to solve a kind of matrix equations over centro-symmetric matrices with a constrained submatrix. The least squares centro-symmetric solutions of the matrix equations with a constrained submatrix can be obtained within a finite number of iterations in the absence of round-off errors, and the least-norm least squares centro-symmetric solution with the constrained submatrix can also be obtained by choosing a special kind of initial matrices. Numerical examples show that the convergence speed of the proposed algorithm is fast.

Key words: central principal submatrix, centro-symmetric solution, submatrix constraint, least squares solution, least norm
solution

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