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Characterizing and computing the Real Radical - An SDP Approach


Ph. Rostalski

Control Group, University of Cambridge, Control Group Seminar 2007

Systems of polynomials play an important role in a variety of applications. Often one is interested in the real points satisfying these equations only. In this talk I will discuss a method (joined work with M. Laurent and J.-B. Lasserre) for computing all points on a zero-dimensional semi-algebraic set described by polynomial equalities and inequalities. Moreover we aim for some "nice" polynomial generators for the vanishing ideal, i.e. for the set of all polynomials vanishing on these points. In contrast to exact computational algebraic methods, the method we propose uses numerical linear algebra and semidefinite optimization to compute approximate solutions to the problem at hand. The main advantage of the proposed method is the real-algebraic nature of the algorithm preventing the need to deal with complex solution components.


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