Iterative Calculation of Sum Of Squares

3 RAPSODI - Reliable numerical approximations of dissipative systems
LPP - Laboratoire Paul Painlevé - UMR 8524, Inria Lille - Nord Europe
Abstract : We propose an iterative algorithm for the calculations of sum of squares of polynomials, reformulated as positive interpolation. The method is based on the definition of a dual functional $G$. The domain of $G$, the boundary of the domain and the boundary at infinity are analyzed in details. In the general case, $G$ is closed convex. For univariate polynomials in the context of the Lukacs representation, $G$ is coercive and strictly convex which yields a unique critical point. Various descent algorithms are evoked. Numerical examples are provided, for univariate and bivariate polynomials.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-01946539
Contributor : Maxime Herda Connect in order to contact the contributor
Submitted on : Friday, December 7, 2018 - 5:53:40 PM
Last modification on : Wednesday, March 23, 2022 - 3:51:22 PM
Long-term archiving on: : Friday, March 8, 2019 - 3:53:12 PM

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• HAL Id : hal-01946539, version 2
• ARXIV : 1812.02444

Citation

Bruno Després, Maxime Herda. Iterative Calculation of Sum Of Squares. 2018. ⟨hal-01946539v2⟩

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