Computing intersections of implicitly specified plane curves

We investigate the application of projection algorithms, more specifically the Douglas-Rachford algorithm, to finding points of intersection of two plane curves. We contrast the employment of typical Euclidean reflection with that of Schwarzian reflection. Local convergence near an isolated. Intersection point is established and the efficacy of the approaches relative to one another and to more classical methods is explored. The extension to curves in higher dimensional space is noted.