In this paper, we present several algorithms for certified homotopy continuation. One typical application is to compute the roots of a zero dimensional system of polynomial equations. We both present algorithms for the certification of single and multiple roots. We also present several ideas for improving the underlying numerical path tracking algorithms, especially in the case of multiple roots.

Authors: Joris van der Hoeven

Keywords: homotopy continuation, polynomial system solving, ball arithmetic, interval arithmetic, reliable computing

A.M.S. subject classification: 65H20, 65H04, 65G20, 30C15, 13P15

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