A prolongation-projection algorithm for computing the finite real variety of an ideal

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dc.creatorLasserre, J. B.
dc.creatorLaurent, M.
dc.creatorRostalski, P.
dc.date2008-06-24
dc.date2009-01-16
dc.date.accessioned2026-07-07T12:30:10Z
dc.date.available2026-07-07T12:30:10Z
dc.descriptionWe provide a real algebraic symbolic-numeric algorithm for computing the real variety $V_R(I)$ of an ideal $I$, assuming it is finite while $V_C(I)$ may not be. Our approach uses sets of linear functionals on $R[X]$, vanishing on a given set of polynomials generating $I$ and their prolongations up to a given degree, as well as on polynomials of the real radical ideal of $I$, obtained from the kernel of a suitably defined moment matrix assumed to be positive semidefinite and of maximum rank. We formulate a condition on the dimensions of projections of these sets of linear functionals, which serves as stopping criterion for our algorithm. This algorithm, based on standard numerical linear algebra routines and semidefinite optimization, combines techniques from previous work of the authors together with an existing algorithm for the complex variety. This results in a unified methodology for the real and complex cases.
dc.descriptionrevised version
dc.identifierhttps://arxiv.org/abs/0806.3874
dc.identifierhttp://arxiv.org/abs/0806.3874
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/216055
dc.subjectAlgebraic Geometry
dc.subjectOptimization and Control
dc.subject14P05; 13P10; 12E12; 12D10; 90C22
dc.titleA prolongation-projection algorithm for computing the finite real variety of an ideal
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