Pascal Koiran

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cs.DS2024

An efficient uniqueness theorem for overcomplete tensor decomposition

Pascal Koiran

We give a new, constructive uniqueness theorem for tensor decomposition. It applies to order 3 tensors of format $n \times n \times p$ and can prove uniqueness of decomposition for…

cs.DS2024

Undercomplete Decomposition of Symmetric Tensors in Linear Time, and Smoothed Analysis of the Condition Number

Pascal Koiran, Subhayan Saha

We study symmetric tensor decompositions, i.e., decompositions of the form $T = \sum_{i = 1}^{r} u_{i}^{\otimes 3}$ where $T$ is a symmetric tensor of order 3 and $u_{i} \in C^{n}$ .…

cs.DS2024

On the uniqueness and computation of commuting extensions

Pascal Koiran

A tuple (Z_1,...,Z_p) of matrices of size r is said to be a commuting extension of a tuple (A_1,...,A_p) of matrices of size n <r if the Z_i pairwise commute and each A_i sits in t…