Abstract
AbstractMotivated by considerations of pure state entanglement in quantum information, we consider the problem of finding the best rank‐1 approximation to an arbitrary r ‐th order tensor. Reformulating the problem as an optimization problem on the Lie group SU (n1) ⊗ … ⊗ SU (nr) of so‐called local unitary transformations and exploiting its intrinsic geometry yields a new approach, which finally leads to Riemannian variant of the conjugate gradient algorithm. Numerical simulations support that our method offers an alternative to the higher‐order power method for computing the best rank‐1 approximation to a tensor. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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