TY - JOUR
T1 - Generalized Singular Value Decompositions for Tensors and Their Applications
AU - He , Zhuo-Heng
AU - Ng , Michael K.
AU - Zeng , Chao
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 692
EP - 713
PY - 2021
DA - 2021/06
SN - 14
DO - http://doi.org/10.4208/nmtma.OA-2020-0132
UR - https://global-sci.org/intro/article_detail/nmtma/19194.html
KW - Multilinear algebra, singular value decomposition, tensor SVD.
AB - <p style="text-align: justify;">In this paper, we consider the generalized singular value decompositions
for two tensors via the T-product. We investigate and discuss in detail the structures of the quotient singular value decomposition (T-QSVD) and product singular
value decomposition (T-PSVD) for two tensors. The algorithms are presented with
numerical examples illustrating the results. For applications, we consider color image watermarking processing with T-QSVD and T-PSVD. There are two advantages
to T-QSVD and T-PSVD approaches on color watermark processing: two color watermarks can be processed simultaneously and only one key needs to be saved.</p>