Title: Characterization and Computation of
Real-Radical Ideals using Semidefinite Programming Techniques
Abstract: In this talk I will
discuss a method (joined work with M. Laurent and J.-B. Lasserre) for
computing all real points on a zero-dimensional semi-algebraic set
described by polynomial equalities and inequalities as well as some
"nice" polynomial generators for the corresponding vanishing ideal,
namely border resp. Gröbner basis for the real radical ideal. In
contrast to exact computational algebraic methods, the method we
propose uses numerical linear algebra and semidefinite optimization
techniques to compute approximate solutions and generator polynomials.
The method is real-algebraic in nature and prevents the computation of
any complex solution. The proposed methods fits well into a relatively
new branch of mathematics called "Numerical Polynomial Algebra".
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