Singular value decomposition is arguably the most powerful tool of numerical linear algebra. It is not surprising that, when compared to the matrix SVD, the tensor generalization is significantly more complicated. For a general third-order tensor we discuss two closely related problems, an SVD-like tensor decomposition and an (approximate) tensor diagonalization. They have many applications in signal processing, blind source separation, and independent component analysis.

Homepage: http://matematika.fkit.hr/erna/

Recent preprints mentioned on the slides:

E. Begovic Kovac: Convergence of a Jacobi-type method for the approximate orthogonal tensor diagonalization

https://arxiv.org/abs/2109.03722

E. Begovic Kovac, A. Boksic: Trace maximization algorithm for the approximate tensor diagonalization

https://arxiv.org/abs/2111.01466