Constructing symmetric nonnegative matrices with prescribed eigenvalues by differential equations
Constructing symmetric nonnegative matrices with prescribed eigenvalues by differential equations
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DOI：
10.1137/0522088
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发表时间：
1991-09
影响因子：
2
通讯作者：
M. Chu;Kenneth R. Driessel
中科院分区：
文献类型：
--
作者：
M. Chu;Kenneth R. Driessel
利用微分方程解对称非负矩阵的逆特征值问题。如果给定的谱是可行的，则只需沿着微分系统的解曲线就可以构造一个对称的非负矩阵。矢量场的选择是基于最小化对称非负矩阵的锥面到由给定谱确定的等谱曲面之间的距离的思想。明确描述了目标函数的投影梯度。利用中心流形理论，还证明了任意解曲线的$\omega$-极限集是单点。文中给出了一些数值算例。
The inverse eigenvalue problem is solved for symmetric nonnegative matrices by means of a differential equation. If the given spectrum is feasible, then a symmetric nonnegative matrix can be constructed simply by following the solution curve of the differential system. The choice of the vector field is based on the idea of minimizing the distance between the cone of symmetric nonnegative matrices and the isospectral surface determined by the given spectrum. The projected gradient of the objective function is explicitly described. Using center manifold theory, it is also shown that the $\omega$-limit set of any solution curve is a single point. Some numerical examples are presented.