@ARTICLE{sael13,
author = {B. Savas and L. Eld{\' e}n},
title = {Krylov-type methods for tensor computations I},
journal = {Linear Algebra and its Applications},
year = {2013},
volume = {438},
pages = {891-918},
abstract = {Several Krylov-type procedures are introduced that generalize
matrix Krylov methods for tensor computations. They are denoted
minimal Krylov recursion, maximal Krylov recursion, and contracted
tensor product Krylov recursion. It is proved that, for a given tensor
A with multilinear rank-(p, q, r), the minimal Krylov recursion extracts
the correct subspaces associated to the tensor in p+q+r number
of tensor-vector-vector multiplications. An optimized minimal
Krylov procedure is described that, for a given multilinear rank of
an approximation, produces a better approximation than the standard
minimal recursion. We further generalize the matrix Krylov
decomposition to a tensor Krylov decomposition. The tensor Krylov
methods are intended for the computation of low multilinear rank
approximations of large and sparse tensors, but they are also useful
for certain dense and structured tensors for computing their higher
order singular value decompositions or obtaining starting points for
the best low-rank computations of tensors. A set of numerical experiments,
using real-world and synthetic data sets, illustrate some
of the properties of the tensor Krylov methods.},
doi = {http://dx.doi.org/10.1016/j.laa.2011.12.007},
issn = {0024-3795},
keywords = {Tensor},
url = {http://www.sciencedirect.com/science/article/pii/S0024379511007877}
}