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    Principal Research Fellow

    LAAS-CNRS, Toulouse, France

    Semidefinite Characterization and Computation of Zero-Dimensional Real Radical Ideals

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    For an ideal I Rx given by a set of generators, a new semidefinite characterization of its real radical I (VR(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 VR(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 bner 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.

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    Description

    Title : Semidefinite Characterization and Computation of Zero-Dimensional Real Radical Ideals
    Author(s) : Jean Bernard Lasserre, Monique Laurent, Philipp Rostalski
    Abstract : For an ideal I Rx given by a set of generators, a new semidefinite characterization of its real radical I (VR(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 VR(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 bner 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.
    Subject : unspecified
    Area : Other
    Language : English
    Year : 2007

    Affiliations LAAS-CNRS, Toulouse, France
    Journal : Foundations of Computational Mathematics
    Volume : 8
    Issue : 5
    Publisher : Springer
    Pages : 607 - 647
    Url : http://www.springerlink.com/index/10.1007/s10208-007-9004-y
    Doi : 10.1007/s10208-007-9004-y

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    Jean's Peer Evaluation activity

    Downloads 14
    Views 75
    Collected by 1
    • Jean Lasserre, Principal Research Fellow, LAAS-CNRS, Toulouse, France.

    Jean has...

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    • Jean Lasserre, Principal Research Fellow, LAAS-CNRS, Toulouse, France.
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