Geodesic
A fast numerical test of multivariate polynomial positiveness with applications
Kybernetika, Tome 54 (2018) no. 2, pp. 289-303.

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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.
DOI : 10.14736/kyb-2018-2-0289
Classification : 12D10, 47N70, 65T50, 65Y20
Keywords: multidimensional systems; positive polynomials; fast Fourier transforms; stability; numerical algorithm 
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Augusta, Petr; Augustová, Petra. A fast numerical test of multivariate polynomial positiveness with applications. Kybernetika, Tome 54 (2018) no. 2, pp. 289-303. doi : 10.14736/kyb-2018-2-0289. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2018-2-0289/

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