165 citations · 445 across the 26 of their papers we have counts for
26 papers
Quantifying low rank approximations of third order symmetric tensors
Shenglong Hu, Defeng Sun, Kim-Chuan Toh
In this paper, we present a method to certify the approximation quality of a low rank tensor to a given third order symmetric tensor. Under mild assumptions, best low rank approxim…
When geometry meets optimization theory: partially orthogonal tensors
Ke Ye, Shenglong Hu
Due to the multi-linearity of tensors, most algorithms for tensor optimization problems are designed based on the block coordinate descent method. Such algorithms are widely employ…
Nondegeneracy of eigenvectors and singular vector tuples of tensors
Shenglong Hu
In this article, nondegeneracy of singular vector tuples, Z-eigenvectors and eigenvectors of tensors is studied. They have found many applications in diverse areas. The main result…
Linear Convergence of an Alternating Polar Decomposition Method for Low Rank Orthogonal Tensor Approximations
Shenglong Hu, Ke Ye
Low rank orthogonal tensor approximation (LROTA) is an important problem in tensor computations and their applications. A classical and widely used algorithm is the alternating pol…
Tensor Norm, Cubic Power and Gelfand Limit
Liqun Qi, Shenglong Hu, Xinzhen Zhang +1
We establish two inequalities for the nuclear norm and the spectral norm of tensor products. The first inequality indicates that the nuclear norm of the square matrix is a matrix n…
Biquadratic Tensors, Biquadratic Decomposition and Norms of Biquadratic Tensors
Liqun Qi, Shenglong Hu, Xinzhen Zhang
Biquadratic tensors play a central role in many areas of science. Examples include elasticity tensor and Eshelby tensor in solid mechanics, and Riemann curvature tensor in relativi…