Approximate decoupling of multivariate polynomials using weighted tensor decomposition. Issue 2 (8th January 2018)

• Record Type: Journal Article
• Authors: Hollander, Gabriel; Dreesen, Philippe; Ishteva, Mariya; Schoukens, Johan
• Is Part Of: Numerical linear algebra with applications. Volume 25:Issue 2(2018)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2018-01-08
• Subjects: multilinear algebra -- multivariate polynomial -- tensor decomposition -- weighted least squares approximation; Algebras, Linear -- Periodicals; 512.5
• DOI: 10.1002/nla.2135
• Languages: English
• ISSNs: 1070-5325

Abstract

Summary: Many scientific and engineering disciplines use multivariate polynomials. Decomposing a multivariate polynomial vector function into a sandwiched structure of univariate polynomials surrounded by linear transformations can provide useful insight into the function while reducing the number of parameters. Such a decoupled representation can be realized with techniques based on tensor decomposition methods, but these techniques have only been studied in the exact case. Generalizing the existing techniques to the noisy case is an important next step for the decoupling problem. For this extension, we have considered a weight factor during the tensor decomposition process, leading to an alternating weighted least squares scheme. In addition, we applied the proposed weighted decoupling algorithm in the area of system identification, and we observed smaller model errors with the weighted decoupling algorithm than those with the unweighted decoupling algorithm.