On the full and block-decoupling of nonlinear functions

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 & Co. KGaA, Weinheim)