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Real Radical Ideals and the Hankel Operator


Ph. Rostalski

UC Berkeley, Discrete Mathematics Seminar (and UC Davis Dec. 8, 2008).

Polynomial equations play an important role in mathematics, engineering and science. Many practical problems can be reduced to computing all real roots of a system of polynomial equations or a certain distinguished basis for the corresponding vanishing ideal. While for the task of computing all complex roots a plethora of algebraic tools is readily available, real root solving is still in its infancy. In this talk we discuss the relation between Hankel operators and real algebraic geometry, more precisely real radical ideals. A new tool for characterizing and computing the real radical ideal is proposed. Based on this characterization, we devise an algorithm using numerical linear algebra and semidefinite optimization to approximately compute the real variety (assuming it is finite) of an ideal as well as a border basis. (Joint work with Jean Lasserre and Monique Laurent).


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