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Semidefinite characterization and computation of real radical ideals


Ph. Rostalski

IMA Annual Program Year Workshop 2007 - Optimization and Control, Institute for Mathematics and its Applications (IMA), University of Minnesota, Minneapolis, MN, USA, Poster

Joint work with J.-B. Lasserre and M. Laurent. For an ideal given by a set of generators, h_1...h_m \in R[x] a new semidefinite characterization of its real radical ideal I(V_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_R=V(I) \subset R^n as well as generators of the real radical ideal. The latter are obtained in the form of border or Gröbner bases. 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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