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Talk

Two-orthogonal tensors: something better than ODECO

  • Emil Horobet (Sapientia Hungarian University of Transylvania)
G3 10 (Lecture hall)

Abstract

In this talk, we study tensors that can be decomposed via successive rank-one approximations. The singular vector tuples of a tensor are the critical points of its best rank-one approximation problem. We study the tensors that can be decomposed by the following procedure: compute a singular vector tuple, subtract it off, compute a singular vector tuple of the new deflated tensor, and repeat. The number of terms in such a decomposition may exceed the rank. Moreover, this decomposition may depend on the order in which terms are subtracted. However, if all singular vectors in the process are orthogonal in at least two factors, then they are all singular vector tuples of the original tensor, and the decomposition is valid independent of order. Tensors that admit such a decomposition are called two-orthogonal and we study the geometry of the variety of these tensors.

Mirke Olschewski

MPI for Mathematics in the Sciences Contact via Mail

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