We study rigidity of rational maps that come from Newton's root finding method for polynomials arbitrary degrees. establish dynamical these maps: each point in the Julia set a Newton map is either rigid (i.e. its orbit can be distinguished combinatorial terms all other orbits), or this eventually lands filled-in polynomial-like restriction original map. As corollary, we show sets many non-trivi...

The problem of minimizing an objective that can be written as the sum of a set of n smooth and strongly convex functions is challenging because the cost of evaluating the function and its derivatives is proportional to the number of elements in the sum. The Incremental Quasi-Newton (IQN) method proposed here belongs to the family of stochastic and incremental methods that have a cost per iterat...