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Quasi-Hankel matrices and the real radical ideal


Ph. Rostalski

CWI Amsterdam, Amsterdam, The Netherlands, CWI-DIAMANT Seminar Combinatorics and Optimization

Polynomial equations play an important role in mathematics, engineering and science and many problems in these fields can be reduced to the task of finding all real roots of a system of polynomial equations. 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 propose (quasi-) Hankel bilinear forms as a new tool for characterizing and computing the real radical ideal and the real variety (assuming it is finite). Based on this characterization, we devise an algorithm using numerical linear algebra and semidefinite optimization to compute approximate solutions to the problem at hand. If time allows we will mention some possible applications to system theory. This talk is based on joined work with Jean Lasserre (LAAS-CNRS) and Monique Laurent (CWI).


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