Low Rank Tensor Decompositions and Approximations

TL;DR

This paper introduces a method using generating polynomials to compute low rank tensor decompositions and approximations, providing quasi-optimal results when tensors are near low rank, advancing tensor analysis techniques.

Contribution

It presents a novel approach leveraging generating polynomials for tensor decompositions and approximations, with theoretical guarantees of quasi-optimality.

Findings

Method achieves quasi-optimal low rank tensor approximation.

Linear relations among tensor entries are expressed by generating polynomials.

Approach is effective when tensors are close to low rank.

Abstract

There exist linear relations among tensor entries of low rank tensors. These linear relations can be expressed by multi-linear polynomials, which are called generating polynomials. We use generating polynomials to compute tensor rank decompositions and low rank tensor approximations. We prove that this gives a quasi-optimal low rank tensor approximation if the given tensor is sufficiently close to a low rank one.