[math-fun] "Solving Cubic Equations By the Quadratic Formula"

FYI -- basins of attraction; Voronoi cells. Given a monic cubic equation p(z)=0, consider the roots r1,r2 of quadratic equation p'(z)=0. Timeshare/interlace 2 Newton methods [z_n+1 = z_n-p(z_n)/p'(z_n)] on quadratic solutions z_0=r1, r2. The Newton method of one of these starting points is guaranteed to converge to a root z_oo=r3 of p(z), i.e., p(r3)=0. Yes, we double the work per iteration, but we are at least guaranteed to converge to one root. Then solve the quadratic p(z)/(z-r3) for the other 2 roots. http://arxiv.org/abs/1401.5148 Bahman Kalantari