Spectral computation with third-order tensors using the t-product

Abstract

The tensor t-product is a powerful tool for the analysis of and computation with third-order tensors. This paper discusses properties and the computation of eigentubes and eigenslices of third-order tensors under the t-product; the eigentubes and eigenslices are analogues of eigenvalues and eigenvectors for matrices. The computational methods considered and analysed include the tensor power method, tensor subspace iteration, and the tensor QR algorithm. Computed examples illustrate the performance of these methods.