Decoupling multivariate functions using a nonparametric filtered tensor decomposition

@article{Decuyper2022DecouplingMF,
  title={Decoupling multivariate functions using a nonparametric filtered tensor decomposition},
  author={Jan Decuyper and Koen Tiels and Siep Weiland and Mark Charles Runacres and Johan Schoukens},
  journal={ArXiv},
  year={2022},
  volume={abs/2205.11153}
}

References

SHOWING 1-10 OF 39 REFERENCES
Decoupling Multivariate Functions Using Second-Order Information and Tensors
TLDR
This article generalizes a tensor-based method for performing decomposition of multivariate vector functions and studies how the use of second-order derivative information can be incorporated, to push the method towards more involved configurations, while preserving uniqueness of the underlying tensor decompositions.
Decoupling Multivariate Polynomials Using First-Order Information and Tensor Decompositions
TLDR
The canonical polyadic decomposition of the three-way tensor of Jacobian matrices directly returns the unknown linear relations as well as the necessary information to reconstruct the univariate polynomials.
Tensor Decompositions and Applications
This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or $N$-way array. Decompositions of higher-order
Swamp reducing technique for tensor decomposition
TLDR
This work presents a new numerical method for tensor analysis based on the iterated Tikhonov regularization and a parameter choice rule that dramatically accelerate the well-known Alternating Least-Squares method.
Decoupling Multivariate Polynomials for Nonlinear State-Space Models
TLDR
Two new polynomial decoupling techniques are introduced and the features and performance of both methods are illustrated on a nonlinear state-space model identified from data of the forced Duffing oscillator.
A Fast Analytical Solution to the Filtered Canonical Polyadic Decomposition Problem
TLDR
It is shown that the originally proposed alternating least squares (ALS) approach can be significantly accelerated through a thorough analysis of one of the matrix factors, that is, the factor that destroys the multilinearity.
...
...