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On the Problem of Decoupling Multivariate Polynomials

  • Stanislav Morozov
  • Dmitry A. ZheltkovEmail author
  • Nikolai Zamarashkin
Conference paper
  • 77 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11958)

Abstract

In this paper we address the application properties of the decoupling multivariate polynomials problem algorithm proposed in [2]. By numerous examples we demonstrate that this algorithm, unfortunately, fails to provide a solution in some cases. Therefore we empirically determine the application scope of this algorithm and show that it is connected with the uniqueness conditions of the CP-decomposition (Canonical Polyadic Decomposition). We also investigate the approximation properties of this algorithm and show that it is capable of construction the best low-rank polynomial approximation provided that the CP-decomposition is unique.

Keywords

Low-parametric representation Polynomial Tensor decomposition 

Notes

Acknowledgements

The work was supported by the Russian Science Foundation, grant 19-11-00338.

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Stanislav Morozov
    • 1
  • Dmitry A. Zheltkov
    • 2
    Email author
  • Nikolai Zamarashkin
    • 2
  1. 1.Lomonosov Moscow State UniversityMoscowRussian Federation
  2. 2.Marchuk Institute of Numerical MathematicsRussian Academy of SciencesMoscowRussian Federation

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