Semidefinite Characterization and Computation of Zero-Dimensional Real Radical Ideals

@article{Lasserre2006SemidefiniteCA,
  title={Semidefinite Characterization and Computation of Zero-Dimensional Real Radical Ideals},
  author={Jean B. Lasserre and Monique Laurent and Philipp Rostalski},
  journal={Foundations of Computational Mathematics},
  year={2006},
  volume={8},
  pages={607-647}
}
Abstract For an ideal I⊆ℝ[x] 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 Gröbner basis. The algorithm… CONTINUE READING

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