A Riemannian variant of the Fletcher-Reeves conjugate gradient method for stochastic inverse eigenvalue problems with partial eigendata
A Riemannian variant of the Fletcher-Reeves conjugate gradient method for stochastic inverse eigenvalue problems with partial eigendata
复制标题
用于具有部分特征数据的随机逆特征值问题的 Fletcher-Reeves 共轭梯度法的黎曼变体
DOI：
10.1002/nla.2221
复制
发表时间：
2019
影响因子：
4.3
通讯作者：
Zhao Zhi
中科院分区：
文献类型：
--
作者：
Yao Teng Teng;Bai Zheng Jian;Zhao Zhi
本文研究了由给定的部分特征值构造随机矩阵的部分特征值随机特征值反问题。针对黎曼流形上的一般无约束极小化问题，提出了一种Fletcher-Reeves共轭梯度法的黎曼变形，并在一定的假设下证明了其全局收敛性.然后，我们将反问题转化为矩阵斜流形上的非线性最小二乘问题，并研究了所提出的几何方法在非线性最小二乘问题中的应用。所提出的几何方法也适用于指定元素和列随机矩阵的情况。最后，数值试验表明，所提出的几何方法是有效的反问题的解决。
In this paper, we focus on the stochastic inverse eigenvalue problem with partial eigendata of constructing a stochastic matrix from the prescribed partial eigendata. A Riemannian variant of the Fletcher–Reeves conjugate gradient method is proposed for solving a general unconstrained minimization problem on a Riemannian manifold, and the corresponding global convergence is established under some assumptions. Then, we reformulate the inverse problem as a nonlinear least squares problem over a matrix oblique manifold, and the application of the proposed geometric method to the nonlinear least squares problem is investigated. The proposed geometric method is also applied to the case of prescribed entries and the case of column stochastic matrix. Finally, some numerical tests are reported to illustrate that the proposed geometric method is effective for solving the inverse problem.