On approximate diagonalization of third order symmetric tensors by orthogonal transformations
Provides theoretical foundations for approximate tensor diagonalization, relevant to tensor decomposition and signal processing.
The paper defines classes of approximately diagonal tensors for third-order symmetric tensors under orthogonal transformations, relates them to Z-eigenvalues/eigenvectors, and proves convergence of the cyclic Jacobi algorithm.
In this paper, we study the approximate orthogonal diagonalization problem of third order symmetric tensors. We define several classes of approximately diagonal tensors, including the ones corresponding to the stationary points of this problem. We study the relationships between these classes, and other well-known objects, such as tensor Z-eigenvalue and Z-eigenvector. We also prove results on convergence of the cyclic Jacobi (or Jacobi CoM2) algorithm.