On the full and block‐decoupling of nonlinear functions. Issue 1 (21st October 2015)

• Record Type: Journal Article
• Authors: Dreesen, Philippe; Ishteva, Mariya; Schoukens, Johan
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 15:Issue 1(2015)
• Page Start: 739
• Page End: 742
• Publication Date: 2015-10-21
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201510352
• Languages: English
• ISSNs: 1617-7061

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>We review a method that decouples multivariate functions into linear combinations of a set of univariate (or simpler multivariate) functions of transformed variables. In this way the given nonlinear multiple‐input‐multiple‐output function is decoupled into a structure having simpler parallel internal branches that are linked by linear transformations to the original inputs and outputs. The procedure collects first‐order information by evaluating the Jacobian matrix of the given function in a set of points. These matrices are stacked into a three‐way tensor, whose decomposition reveals the decoupled representation. (© 2015 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)</p> </abstract>