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Semidefinite Characterization and Computation of Real Radical Ideals


Ph. Rostalski

IfA Internal Seminar Series

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, which are intrinsically computationally demanding, the method we propose uses numerical linear algebra and semidefinite optimization to compute approximate solutions to the problem at hand. Another advantage of the proposed method is the real-algebraic nature of the algorithm preventing the need to deal with complex solutions components. The proposed methods fits well in a relatively new branch of mathematics called "Numerical Polynomial Algebra".


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