2019/09/04 by Liqun Qi, Shenglong Hu, Qi, Liqun +1
Chemistry · Mathematics · #Advanced NMR Techniques and Applications #FOS: Mathematics #Numerical Analysis (math.NA) #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.1909.01529
openalex publication_date 2019/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 tensor is equal to the square root of the spectral norm of three positive semi-definite biquadratic tensors, and the square roots of the nuclear norms of those three positive semi-definite biquadratic tensors are lower bounds of the nuclear norm of that third order tensor. This provides a way to estimate and to evaluate the spectral norm and the nuclear norm of that third order tensor. Some upper and lower bounds for the spectral norm and nuclear norm of a third order tensor, by spectral radii and nuclear norms of some symmetric matrices, are presented.