A fast numerical test of multivariate polynomial positiveness with applications

Petr Augusta; Petra Augustová

Kybernetika (2018)

  • Volume: 54, Issue: 2, page 289-303
  • ISSN: 0023-5954

Abstract

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The paper presents a simple method to check a positiveness of symmetric multivariate polynomials on the unit multi-circle. The method is based on the sampling polynomials using the fast Fourier transform. The algorithm is described and its possible applications are proposed. One of the aims of the paper is to show that presented algorithm is significantly faster than commonly used method based on the semi-definite programming expression.

How to cite

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Augusta, Petr, and Augustová, Petra. "A fast numerical test of multivariate polynomial positiveness with applications." Kybernetika 54.2 (2018): 289-303. <http://eudml.org/doc/294612>.

@article{Augusta2018,
abstract = {The paper presents a simple method to check a positiveness of symmetric multivariate polynomials on the unit multi-circle. The method is based on the sampling polynomials using the fast Fourier transform. The algorithm is described and its possible applications are proposed. One of the aims of the paper is to show that presented algorithm is significantly faster than commonly used method based on the semi-definite programming expression.},
author = {Augusta, Petr, Augustová, Petra},
journal = {Kybernetika},
keywords = {multidimensional systems; positive polynomials; fast Fourier transforms; stability; numerical algorithm},
language = {eng},
number = {2},
pages = {289-303},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A fast numerical test of multivariate polynomial positiveness with applications},
url = {http://eudml.org/doc/294612},
volume = {54},
year = {2018},
}

TY - JOUR
AU - Augusta, Petr
AU - Augustová, Petra
TI - A fast numerical test of multivariate polynomial positiveness with applications
JO - Kybernetika
PY - 2018
PB - Institute of Information Theory and Automation AS CR
VL - 54
IS - 2
SP - 289
EP - 303
AB - The paper presents a simple method to check a positiveness of symmetric multivariate polynomials on the unit multi-circle. The method is based on the sampling polynomials using the fast Fourier transform. The algorithm is described and its possible applications are proposed. One of the aims of the paper is to show that presented algorithm is significantly faster than commonly used method based on the semi-definite programming expression.
LA - eng
KW - multidimensional systems; positive polynomials; fast Fourier transforms; stability; numerical algorithm
UR - http://eudml.org/doc/294612
ER -

References

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