非负逆特征值问题的黎曼近似牛顿-共轭梯度方法：非对称情况
A Riemannian Inexact Newton-CG Method for Nonnegative Inverse Eigenvalue Problems: Nonsymmetric Case
AI总结：
本文提出一种非负逆特征值问题的黎曼近似牛顿-共轭梯度方法，用于求解非对称情况下的非负矩阵，其谱为给定的自共轭复数集。
摘要：
本文研究了寻找非负矩阵使其谱为给定自共轭复数集的非负逆特征值问题。我们首先将该问题转化为多个矩阵流形上的欠定约束非线性矩阵方程。然后提出了一种黎曼近似牛顿-共轭梯度方法来求解非线性矩阵方程。在某些温和条件下，所提出的方法具有全局和二次收敛性。我们还将该方法扩展到预设条目的情况。最后，报告了数值实验以说明所提方法的效率。
英文摘要：
This paper is concerned with the nonnegative inverse eigenvalue problem of finding a nonnegative matrix such that its spectrum is the prescribed self-conjugate set of complex numbers. We first reformulate the nonnegative inverse eigenvalue problem as an under-determined constrained nonlinear matrix equation over several matrix manifolds. Then we propose a Riemannian inexact Newton-CG method for solving the nonlinear matrix equation. The global and quadratic convergence of the proposed method is established under some mild conditions. We also extend the proposed method to the case of prescribed entries. Finally, numerical experiments are reported to illustrate the efficiency of the proposed method.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
