A Riemannian inexact Newton dogleg method for constructing a symmetric nonnegative matrix with prescribed spectrum

This paper is concerned with the inverse problem of constructing a symmetric nonnegative matrix from realizable spectrum. We reformulate as an underdetermined nonlinear equation over Riemannian product manifold. To solve it, we develop inexact Newton dogleg method for solving general defined between manifolds and Euclidean spaces. The global quadratic convergence proposed established under some mild assumptions. Then, by applying to its equivalent preconditioner perturbed normal also constructed. Numerical tests show efficiency problem.