@ARTICLE{elsa09,
  author = {L. Eld\'en and B. Savas},
  title = {A {Newton--Grassmann} method for computing the Best Multi-Linear
	Rank-(${r}_1,r_2,r_3$) Approximation of a Tensor},
  journal = {SIAM J. Matrix Anal. Appl.},
  year = {2009},
  volume = {31},
  pages = {248-271},
  abstract = {We derive a Newton method for computing the best rank-$(r_1,r_2,r_3)$
	approximation of a given $J \x K \x L$ tensor $\cA$. The problem
	is formulated as an approximation problem on a product of Grassmann
	manifolds. Incorporating the manifold structure into Newton's method
	ensures that all iterates generated by the algorithm are points on
	the Grassmann manifolds. We also introduce a consistent notation
	for matricizing a tensor, for contracted tensor products and some
	tensor-algebraic manipulations, which simplify the derivation of
	the Newton equations and enable straightforward algorithmic implementation.
	Experiments show a quadratic convergence rate for the Newton-Grassmann
	algorithm.},
  file = {elsa09.pdf:elsa09.pdf:PDF}
}