Polynomial homotopy continuation methods solve polynomial systems in two stages. In the first stage, a homotopy method constructs a family of polynomial systems, connecting the input system to a system with known solutions. In the second stage, a continuation method tracks the solution paths originating at the known solutions, leading to the solutions of the input system. New trends in polynomial homotopy continuation will be presented.
SIAM AG 2021, 18 August 2021, online