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Approximate decoupling of multivariate polynomials using weighted tensor decomposition
Author(s) -
Hollander Gabriel,
Dreesen Philippe,
Ishteva Mariya,
Schoukens Johan
Publication year - 2018
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2135
Subject(s) - univariate , decoupling (probability) , mathematics , multivariate statistics , tensor (intrinsic definition) , polynomial , algorithm , tensor decomposition , explained sum of squares , mathematical optimization , pure mathematics , mathematical analysis , statistics , control engineering , engineering
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.