@ARTICLE{elsa11,
  author = {L. Eld\'en and B. Savas},
  title = {Perturbation Theory and Optimality Conditions for the Best Multilinear
	Rank Approximation of a Tensor},
  journal = {SIAM J. Matrix Anal. Appl., to appear},
  year = {2011},
  volume = {32},
  pages = {1422-1450},
  abstract = {The problem of computing the best rank-$(p,q,r)$ approximation of
	a third order tensor is considered. First the problem is reformulated
	as a maximization problem on a product of three Grassmann manifolds.
	Then expressions for the gradient and the Hessian are derived in
	a local coordinate system at a stationary point, and conditions for
	a local maximum are given. A first order perturbation analysis is
	performed using the Grassmann manifold framework. The analysis is
	illustrated in a few examples, and it is shown that the perturbation
	theory for the singular value decomposition is a special case of
	the tensor theory.},
  doi = {http://dx.doi.org/10.1137/110823298},
  file = {elsa11.pdf:elsa11.pdf:PDF},
  keywords = {tensor, multilinear rank, best rank-$(p, q, r)$ approximation, perturbation
	theory, first order optimality conditions, second order optimality
	conditions, Grassmann manifold, stationary point},
  owner = {laeld},
  timestamp = {2011.03.11},
  url = {http://epubs.siam.org.lt.ltag.bibl.liu.se/sima/resource/1/sjmael/v32/i4/p1422_s1}
}