线性矩阵方程的斜, Hermit{<i>P</i>, <i>k</i>+1}, Hamilton解

雍进军; 陈果良; 徐伟孺

doi:10.3969/j.issn.1000-5641.2018.04.004

线性矩阵方程的斜, Hermit{P, k+1}, Hamilton解

doi: 10.3969/j.issn.1000-5641.2018.04.004

雍进军^1,2,,
陈果良^2, ,,
徐伟孺²

1.
贵州师范学院数学与计算机科学学院, 贵阳 550018
2.
华东师范大学数学科学学院, 上海 200241

基金项目:

国家自然科学基金 11471122

2016年度贵州省科技平台及人才团队专项基金项目黔科合平台人才【2016】5609

贵州师范学院校级课题 2015BS009

详细信息

作者简介:
雍进军, 男, 副教授, 研究方向为计算数学.E-mail:yongjinjun@126.com

通讯作者:
陈果良, 男, 教授, 博士生导师, 研究方向为数值代数.E-mail:glchen@math.ecnu.edu.cn

中图分类号: O241.6
计量
- 文章访问数: 137
- HTML全文浏览量: 29
- PDF下载量: 281
- 被引次数: 0
出版历程
- 收稿日期: 2017-07-19
- 刊出日期: 2018-07-25

The skew-Hermitian {P, k+1} Hamiltonian solutions of a linear matrix equation

YONG Jin-jun^{1,2
,},
CHEN Guo-liang^{2
, ,},
XU Wei-ru²

1.
Department of Mathematics and Computer Science, Guizhou Education University, Guiyang 550018, China
2.
School of Mathematical Sciemces, East China Normal University, Shanghai 200241, China

摘要

摘要: 给定矩阵$P\in {\rm {\bf C}}^{n\times n}$且$P^\ast =-P=P^{k+1}$.考虑了矩阵方程$AX=B$存在斜Hermite$\{P, k+1\}$ (斜) Hamilton解的充要条件, 并给出了解的表达式.进一步, 对于任意给定的矩阵$\tilde {A}\in {\rm {\bf C}}^{n\times n}$, 给出了使得Frobenius范数$\vert \vert \tilde {A}-\bar {A}\vert \vert $取得最小值的最佳逼近解$\bar {A}\in {\rm {\bf C}}^{n\times n}$.当矩阵方程$AX=B$不相容时, 给出了斜Hermite$\{P, k+1\}$ (斜) Hamilton最小二乘解, 在此条件下, 给出了对于任意给定矩阵的最佳逼近解.最后给出一些数值实例.
- 斜Hermite矩阵 /
- Hamilton矩阵 /
- 最小二乘解 /
- 斜Hermite{P, k+1}Hamilton矩阵
Abstract: Given $P\in {\rm {\bf C}}^{n\times n}$ and $P^\ast =-P=P^{k+1}$, we consider the necessary and sufficient conditions such that the matrix equation $AX=B$ is consistent with the skew-Hermitian $\{P, k+1\}$ (skew-) Hamiltonian structural constraint. Then, the corresponding expressions of the constraint solutions are also obtained. For any given matrix $\tilde {A}\in {\rm {\bf C}}^{n\times n}$, we present the optimal approximate solution $\bar {A}\in {\rm {\bf C}}^{n\times n}$ such that ${\vert}{\vert }\tilde {A}-\bar {A}\vert \vert $ is minimized in the Frobenius norm sense. If the matrix equation $AX=B$ is not consistent, its least-squares skew-Hermitian $\{P, k+1\}$ (skew-) Hamiltonian solutions are given. Under the least-square sense, we consider the best approximate solutions to any given matrix. Finally, some illustrative experiments are also presented.
- skew-Hermitian matrix /
- Hamiltonian matrix /
- least-squares solution /
- skew-Hermitian{P, k+1}Hamiltonian matrix

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参考文献(18)

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