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Semidefinite Characterization and Computation of Real Radical Ideals

Author(s):

J.B. Lasserre, M. Laurent, Ph. Rostalski
Conference/Journal:

Foundations of Computational Mathematics, vol. 8, no. 5, pp. 607-647, MSC-class: 14P05; 13P10 (primary); 12E12; 12D10; 90C22 (secondary)
Abstract:

For an ideal $I\subseteq\mathbb{R}[x]$ given by a set of generators, a new semidefinite characterization of its real radical $I(V_\mathbb{R}(I))$ is presented, provided it is zero-dimensional (even if $I$ is not). Moreover we propose an algorithm using numerical linear algebra and semidefinite optimization techniques, to compute all (finitely many) points of the real variety $V_\mathbb{R}(I)$ as well as a set of generators of the real radical ideal. The latter is obtained in the form of a border or Gr\"obner basis. The algorithm is based on moment relaxations and, in contrast to other existing methods, it exploits the real algebraic nature of the problem right from the beginning and avoids the computation of complex components.

Further Information
Year:

2008
Type of Publication:

(01)Article
Supervisor:



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% Autogenerated BibTeX entry
@Article { LasLau:2008:IFA_2482,
    author={J.B. Lasserre and M. Laurent and Ph. Rostalski},
    title={{Semidefinite Characterization and Computation of Real
	  Radical Ideals}},
    journal={Foundations of Computational Mathematics},
    year={2008},
    volume={8},
    number={5},
    pages={607--647},
    month=sep,
    url={http://control.ee.ethz.ch/index.cgi?page=publications;action=details;id=2482}
}
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