东北大学学报:自然科学版 ›› 2017, Vol. 38 ›› Issue (6): 909-912.DOI: 10.12068/j.issn.1005-3026.2017.06.029

• 数学 • 上一篇    

一类Sylvester矩阵方程的迭代解法

邵新慧, 彭程   

  1. (东北大学 理学院, 辽宁 沈阳110819)
  • 收稿日期:2015-12-30 修回日期:2015-12-30 出版日期:2017-06-15 发布日期:2017-06-11
  • 通讯作者: 邵新慧
  • 作者简介:邵新慧(1970-),女,山东青岛人,东北大学副教授,博士.
  • 基金资助:
    国家自然科学基金资助项目(11071033).

Iterative Solutions to Sylvester Matrix Equations

SHAO Xin-hui, PENG Cheng   

  1. School of Sciences, Northeastern University, Shenyang 110819, China.
  • Received:2015-12-30 Revised:2015-12-30 Online:2017-06-15 Published:2017-06-11
  • Contact: SHAO Xin-hui
  • About author:-
  • Supported by:
    -

摘要: 针对Sylvester矩阵方程给出了一种基于梯度的迭代解法.通过引入一个松弛参数和应用层次识别原理,构建了一种新型的迭代方法求解一类Sylvester矩阵方程.收敛分析表明,在一定的假设条件下对于任意初始值,迭代解都收敛到精确解.数值算例也表明了所给方法的有效性和优越性.

关键词: Sylvester矩阵方程, 迭代解法, 梯度, 收敛, 松弛参数

Abstract: The gradient-based iterative solutions to Sylvester matrix equations are given. By introducing a relaxation parameter and applying the hierarchical identification principle, an iterative algorithm is constructed to solve Sylvester matrix equations. Convergence analysis indicates that the iterative solutions converge with the exact solutions to any initial value under certain assumptions. Numerical examples are given to testify the efficiency of the proposed method.

Key words: Sylvester matrix equation, iterative solution, gradient, convergence, relaxation parameter

中图分类号: