A Riemannian variant of the Fletcher–Reeves conjugate gradient method for stochastic inverse eigenvalue problems with partial eigendata
Teng‐Teng Yao, Zheng‐Jian Bai, Zhi Zhao · Numerical Linear Algebra with Applications · 2018
Summary 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.