Three decompositions of symmetric tensors have similar condition numbers

TL;DR

This paper explores the relationships between the condition numbers of three symmetric tensor decompositions and demonstrates how understanding these relations can significantly accelerate their computation.

Contribution

It establishes a connection between the condition numbers of different symmetric tensor decompositions and proposes a method to compute them more efficiently.

Findings

Condition numbers of three tensor decompositions are related.

The proposed approach speeds up condition number computation by orders of magnitude.

Improved understanding of tensor decomposition stability.

Abstract

We relate the condition numbers of computing three decompositions of symmetric tensors: the canonical polyadic decomposition, the Waring decomposition, and a Tucker-compressed Waring decomposition. Based on this relation we can speed up the computation of these condition numbers by orders of magnitude