Details:
Title  Semidefinite characterization and computation of zerodimensional real radical ideals.  Author(s)  JeanBernard Lasserre, Monique Laurent, Philipp Rostalski  Type  Article in Journal  Abstract  For an ideal I⊆ℝ[x] given by a set of generators, a new semidefinite characterization of its real radical I(V ℝ(I)) is presented, provided it is zerodimensional (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(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 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.  Keywords  Algebraic geometry, Zerodimensional ideal (Real), radical ideal  ISSN  16153375; 16153383/e 
URL 
http://link.springer.com/article/10.1007%2Fs102080079004y 
Language  English  Journal  Found. Comput. Math.  Volume  8  Number  5  Pages  607647  Publisher  Springer US, New York, NY  Year  2008  Edition  0  Translation 
No  Refereed 
No 
