QLunch: On best rank-k approximations to tensors
Speaker: Jan Draisma from Universität Bern
Title: On best rank-k approximations to tensors
By the Eckart-Young Theorem, the best rank-k approximation to a matrix A is the sum of rank-one matrices corresponding to the k largest singular values of A. The corresponding statement for tensors is, alas, false. I will discuss two variants:
1. The first concerns orthogonally decomposable tensors. These are particularly pleasant tensors for which the Eckart-Young theorem is true without modification.
2. The second concerns all tensors, but the Eckart-Young theorem is weakened to the statement that the best rank-k approximation lies in the linear span of the critical rank-one approximations. This talk is based on joint work with Boralevi-Horobet-Robeva and with Ottaviani-Tocino.