论文标题
Riemannian Newton-CG方法用于从光谱数据中构建阳性随机基质
Riemannian Newton-CG Methods for Constructing a Positive Doubly Stochastic Matrix From Spectral Data
论文作者
论文摘要
在本文中，我们考虑了正偶有随机矩阵的逆特征值问题，该问题旨在从规定的可实现的光谱数据中构建一个积极的双随机矩阵。通过使用真实的Schur分解，逆问题将作为矩阵乘积歧管上的非线性矩阵方程式写入。我们提出了单调和非单调的riemannian不切实际的牛顿-CG方法，用于求解非线性基质方程。提出的方法的全局和二次收敛是在某些假设下建立的。我们还基于计算的实际SCHUR分解为逆问题提供了构造解决方案的不变子空间。最后，我们报告了一些数值测试，包括在Digraph中的应用，以说明所提出的方法的有效性。
In this paper, we consider the inverse eigenvalue problem for the positive doubly stochastic matrices, which aims to construct a positive doubly stochastic matrix from the prescribed realizable spectral data. By using the real Schur decomposition, the inverse problem is written as a nonlinear matrix equation on a matrix product manifold. We propose monotone and nonmonotone Riemannian inexact Newton-CG methods for solving the nonlinear matrix equation. The global and quadratic convergence of the proposed methods is established under some assumptions. We also provide invariant subspaces of the constructed solution to the inverse problem based on the computed real Schur decomposition. Finally, we report some numerical tests, including an application in digraph, to illustrate the effectiveness of the proposed methods.
