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TitleSemidefinite characterization and computation of zero-dimensional real radical ideals.
Author(s) Jean-Bernard Lasserre, Monique Laurent, Philipp Rostalski
TypeArticle in Journal
AbstractFor 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 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(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.
KeywordsAlgebraic geometry, Zero-dimensional ideal (Real), radical ideal
ISSN1615-3375; 1615-3383/e
URL http://link.springer.com/article/10.1007%2Fs10208-007-9004-y
LanguageEnglish
JournalFound. Comput. Math.
Volume8
Number5
Pages607--647
PublisherSpringer US, New York, NY
Year2008
Edition0
Translation No
Refereed No
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