6 papers
Some Tucker-like approximations based on the modal semi-tensor product
Ze-Jia Xie, Xiao-Qing Jin, Zhi Zhao
Approximating higher-order tensors by the Tucker format has been applied in many fields such as psychometrics, chemometrics, signal processing, pattern classification, and so on. I…
A Riemannian Inexact Newton Dogleg Method for Constructing a Symmetric Nonnegative Matrix with Prescribed Spectrum
Zhi Zhao, Teng-Teng Yao, Zheng-Jian Bai +1
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 n…
A Riemannian Derivative-Free Polak-Ribiere-Polyak Method for Tangent Vector Field
Teng-Teng Yao, Zhi Zhao, Zheng-Jian Bai +1
This paper is concerned with the problem of finding a zero of a tangent vector field on a Riemannian manifold. We first reformulate the problem as an equivalent Riemannian optimiza…
Riemannian Inexact Newton Method for Structured Inverse Eigenvalue and Singular Value Problems
Chun-Yueh Chiang, Matthew M. Lin, Xiao-Qing Jin
Inverse eigenvalue and singular value problems have been widely discussed for decades. The well-known result is the Weyl-Horn condition, which presents the relations between the ei…
A Preconditioned Riemannian Gauss-Newton Method for Least Squares Inverse Eigenvalue Problems
Teng-Teng Yao, Zheng-Jian Bai, Xiao-Qing Jin +1
This paper is concerned with the least squares inverse eigenvalue problem of reconstructing a linear parameterized real symmetric matrix from the prescribed partial eigenvalues in…
A Riemannian Inexact Newton-CG Method for Nonnegative Inverse Eigenvalue Problems: Nonsymmetric Case
Zhi Zhao, Zheng-Jian Bai, Xiao-Qing Jin
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 numbe…