Weighted tensor decomposition for approximate decoupling of multivariate polynomials

TL;DR

This paper introduces a weighted tensor decomposition method for approximate decoupling of multivariate polynomials, extending existing techniques to handle noisy data and improving system identification accuracy.

Contribution

It generalizes tensor-based polynomial decoupling to noisy scenarios by incorporating a weight factor, enhancing practical applicability.

Findings

Smaller model errors in system identification

Effective handling of noisy polynomial data

Improved tensor decomposition accuracy

Abstract

Multivariate polynomials arise in many different disciplines. Representing such a polynomial as a vector of univariate polynomials can offer useful insight, as well as more intuitive understanding. For this, techniques based on tensor methods are known, but these have only been studied in the exact case. In this paper, we generalize an existing method to the noisy case, by introducing a weight factor in the tensor decomposition. Finally, we apply the proposed weighted decoupling algorithm in the domain of system identification, and observe smaller model errors.