Two-sided diagonalization of order-three tensors

This paper presents algorithms for two-sided diagonalization of order-three tensors. It is another expression for joint non-symmetric approximate diagonalization of a set of square ma trices, say T₁,..., T_M: We seek two non-orthogonal matrices A and B such that the products AT_mB^T are close to diagonal in a sense. The algorithms can be used for a block tensor decomposition and applied e.g. for tensor deconvolution and feature extraction using the convolutive model.