Krylov subspace methods for large multidimensional eigenvalue computation

In this paper, we describe some Krylov subspace methods for computing eigentubes and eigenvectors (eigenslices) for large and sparse third-order tensors. This work provides projection methods for computing some of the largest (or smallest) eigentubes and eigenslices using the t-product. In particular, we use the tensor Arnoldi's approach for the non-hermitian case and the tensor Lanczos's approach for f-hermitian tensors. We also use the tensor block Arnoldi method to approximate the extreme eigentubes of a large tensor. Computed examples are given to illustrate the effectiveness of these methods.