2021/10/29 by Zhi Zhao, Zhao, Zhi, Teng-Teng Yao +8
Computer Science · Engineering · Mathematics · #15A18 #65F08 #65F15 #65F18 #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Optical Polarization and Ellipsometry #cs.NA #math.NA #msc:15A18 #msc:65F08 #msc:65F15 #msc:65F18
paper · pdf · doi:10.48550/arxiv.2110.15749
32 pages, 6 figures
arxiv created 2021/10/29 · openalex publication_date 2021/10/29 · arxiv updated 2021/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is concerned with the inverse problem of constructing a symmetric nonnegative matrix from realizable spectrum. We reformulate the inverse problem as an underdetermined nonlinear matrix equation over a Riemannian product manifold. To solve it, we develop a Riemannian underdetermined inexact Newton dogleg method for solving a general underdetermined nonlinear equation defined between Riemannian manifolds and Euclidean spaces. The global and quadratic convergence of the proposed method is established under some mild assumptions. Then we solve the inverse problem by applying the proposed method to its equivalent nonlinear matrix equation and a preconditioner for the perturbed normal Riemannian Newton equation is also constructed. Numerical tests show the efficiency of the proposed method for solving the inverse problem.