A polynomial homotopy h(x,t) = 0, is a family of polynomial systems in x, where t is one parameter. The homotopy defines solution paths x(t). We consider the problem of tracking paths moving to a singularity, which may be isolated or not, which may be at infinity or not.
Recent work (presented at CASC 2022) demonstrated the effectiveness of Richardson extrapolation to accurately compute the value of the parameter t in the homotopy, corresponding to the nearest singular solution.
Preliminary computations shows the promise of Aitken extrapolation to accurately compute the coordinates x of the singular solution.
This is joint work with Kylash Viswanathan.
JMM 2023, 6 January 2023, Boston, MA