@Article{NMTMA-14-3, author = {Zeng, Chao and Zhuo-Heng, He and Ng, Michael, K. and Zeng, Chao}, title = {Generalized Singular Value Decompositions for Tensors and Their Applications}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2021}, volume = {14}, number = {3}, pages = {692--713}, abstract = {
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.
}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2020-0132}, url = {https://global-sci.com/article/90316/generalized-singular-value-decompositions-for-tensors-and-their-applications} }