对称正双随机矩阵的特征值反问题  

Inverseeigenvalue problem of symmetric positive doubly stochasticmatrix

作　　者：曾琴 赵志 ZENG Qin;ZHAO Zhi(School of Sciences,Hangzhou Dianzi University,Hangzhou Zhejiang 310018,China)

机构地区：[1]杭州电子科技大学理学院,浙江杭州310018

出　　处：《杭州电子科技大学学报（自然科学版）》2023年第5期84-89,共6页Journal of Hangzhou Dianzi University：Natural Sciences

基　　金：浙江省自然科学基金资助项目(LY21A010010)。

摘　　要：研究给定部分特征对的对称正双随机矩阵的特征值反问题。首先,将该反问题等价表述为特殊的黎曼流形到欧氏空间的欠定矩阵方程求解问题;然后,运用非单调黎曼非精确牛顿CG方法求解此方程,通过分析得到对应欠定映射的微分算子是满射的等价条件。数值实验结果表明,非单调黎曼非精确牛顿CG方法可以稳定有效地解决这类反问题。The inverse eigenvalue problem of symmetric positive double stochastic matrices with given partial eigendata is studied.Firstly,this inverse problem is formulated as an equivalent problem of solving an underdetermined equation from a special Riemannian manifold to a Euclidean space.Then,the non-monotone Riemannian inexact Newton CG method is applied to solve the above equation.Surjectivity condition of the differential of the underling nonlinear map is also discussed.Finally,numerical results show that the nonmonotone Riemann inexact Newton CG method can effectively solve this kind of inverse problem.

关 键 词：特征值反问题 对称正双随机矩阵 黎曼流形 黎曼非精确牛顿CG方法 

分 类 号：O241.6[理学—计算数学]