165 citations · 445 across the 26 of their papers we have counts for
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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…
Spectral Norm and Nuclear Norm of a Third Order Tensor
Liqun Qi, Shenglong Hu
The spectral norm and the nuclear norm of a third order tensor play an important role in the tensor completion and recovery problem. We show that the spectral norm of a third order…
Generating Hypergraphs, Decomposability and Classification of Two-Step Nilpotent Lie Algebras
Shenglong Hu, Liqun Qi, Honglian Zhang
In 1973, Gauger proposed a generator-relation method and a duality theory for two-step nilpotent Lie algebras. Based upon these, he classified two-step nilpotent Lie algebras of di…