Título: Finding real zeros a lot faster through an adaptive grid

Palestrante: Josué Tonelli Cueto (INRIA)
Data: 09/07/2021
Horário: 09:00h
Local: Transmissão via RNP e Youtube

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Resumo: An algorithm by Cucker, Krick, Malajovich and Wschebor finds all the real zeros of a dense real polynomial system. This algorithm has three very important properties for a numerical algorithm in algebraic geometry: 1) numerically stable, 2) parallelizable, and 3) good probabilistic run-time. Unfortunately, the algorithm does not have a finite expected run-time, a fact that has been inherited by all algorithms in real numerical algebraic geometry. In this talk, we show how by making this algorithm adaptive, we can obtain finite expected run-time while preserving all the nice features of the original algorithm.