Block-Decoupling Multivariate Polynomials Using the Tensor Block-Term Decomposition
We present a tensor-based method to decompose a given set of multivariate functions into linear combinations of a set of multivariate functions of linear forms of the input variables. The method proceeds by forming a three-way array (tensor) by stacking Jacobian matrix evaluations of the function behind each other. It is shown that a block-term decomposition of this tensor provides the necessary information to block-decouple the given function into a set of functions with small input-output dimensionality. The method is validated on a numerical example.
KeywordsMultivariate polynomials Multilinear algebra Tensor decomposition Block-term decomposition Waring decomposition
This work was supported in part by the Fund for Scientific Research (FWO-Vlaanderen), by the Flemish Government (Methusalem), by the Belgian Government through the Inter-university Poles of Attraction (IAP VII) Program, by the ERC Advanced Grant SNLSID under contract 320378, by the ERC Advanced Grant BIOTENSORS under contract 339804, by the ERC Starting Grant SLRA under contract 258581, by the Research Council KU Leuven: CoE PFV/10/002 (OPTEC), by FWO projects G.0830.14N, G.0881.14N, and G.0280.15N and by the Belgian Federal Science Policy Office: IUAP P7/19 (DYSCO II, Dynamical systems, control and optimization, 2012–2017). Mariya Ishteva is an FWO Pegasus Marie Curie Fellow.
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