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Attasi ND systems, polynomial system solving and algebraic optimization

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If you have a question about this talk, please contact Tim Hughes.

This talk will unify the results about the eigenvalue approach to polynomial system solving from the Attasi ND systems standpoint. In fact one needs to use autonomous Attasi ND systems which were not really defined in Attasi’s original paper. But once that is done the so-called Stetter matrices of a polynomial system with finite number of solutions (over the complex numbers) follow directly from Attasiā€™s realization theory.

I will then discuss the approach followed in the work with Bleylevens and Peeters on determining the solutions of systems of polynomial equations using large eigenvalue solvers, where we use recursive solution of the ND system equations to obtain the result of the action of the shift matrices on the initial state. I will also describe possibilities for computing these recursions on a FPGA chip by using the FIFO (first-in-first-out) facility.

This talk is part of the CUED Control Group Seminars series.

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