On the condition number of the tensor rank decomposition

by Nick Vannieuwenhoven (KU Leuven)

Location: 200B.02.18, Leuven
Time: Thursday December 6, 2018 at 14:00

The tensor rank decomposition or CPD expresses a tensor as a minimum-length linear combination of elementary rank-1 tensors. It has found application in fields as diverse as psychometrics, chemometrics, signal processing and machine learning, mainly for data analysis purposes. In these applications, the theoretical model is often a low-rank CPD and the elementary rank-1 tensors are usually the quantity of interest. However, in practice, this model is always corrupted by measurement errors. In order to understand how sensitive the elementary constituents of a CPD are to perturbations of the tensor, the fundamental concept of the condition number was proposed in numerical analysis. In this talk, we will investigate the condition number of the CPD. Moreover it will be shown that the most popular class of non-iterative algorithms for computing CPDs is numerically unstable.

This is joint work with C. Beltrán (Universidad de Cantabria) and P. Breiding (MPI MiS Leipzig).