In this work, we investigate a model-order reduction scheme for polynomial systems. We begin with defining the generalized multivariate transfer functions for the system. Based on this, we aim at constructing a reduced-order system, interpolating the defined generalized transfer functions at a given set of interpolation points. Furthermore, we provide a method, inspired by the Loewner approach for linear and (quadratic-)bilinear systems, to determine a good-quality reduced-order system in an automatic way. We also discuss the computational issues related to the proposed method and a potential application of a CUR matrix approximation in order to further speed up simulation of the reduced-order systems. We test the efficiency of the proposed method via two benchmark examples.


  1. model order reduction
  2. polynomial dynamical systems
  3. transfer functions
  4. interpolation
  5. tensor algebra
  6. matricization

MSC codes

  1. 15A69
  2. 34C20
  3. 41A05
  4. 49M05
  5. 93A15
  6. 93C10
  7. 93C15

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Information & Authors


Published In

cover image SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Pages: A84 - A108
ISSN (online): 1095-7197


Submitted: 30 April 2019
Accepted: 23 September 2020
Published online: 5 January 2021


  1. model order reduction
  2. polynomial dynamical systems
  3. transfer functions
  4. interpolation
  5. tensor algebra
  6. matricization

MSC codes

  1. 15A69
  2. 34C20
  3. 41A05
  4. 49M05
  5. 93A15
  6. 93C10
  7. 93C15



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