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...

introduction: the aim of this study was to evaluate the effect of proximal contour of class ii composite restorations placed with straight or contoured matrix band using composite resins with different modulus of elasticity on stress distribution by finite element method. methods: in order to evaluate the stress distribution of class ii composite restorations using finite element method, upper ...

1. The number of zeroes of a polynomial over a finite field 1 2. Interpretation in terms of zeta functions 3 2.1. Eigenvalues in the smooth case 4 2.2. Some easy examples 5 3. The Newton polygon 7 3.1. Newton polygons in families 8 4. Abstract Hodge polygons and Newton polygons 9 5. Results of Deligne, Katz, Mazur and Ogus 10 6. Some special cases 11 6.1. Abelian varieties 11 6.2. Curves 12 Ref...

It has long been known that variational inequality problems can be reformulated as nonsmooth equations. Recently, locally high-order convergent nonsmooth Newton methods for nonsmooth equations have been well established via the concept of semismoothness. In this paper, we focus our discussions on a way of globalizing nonsmooth Newton methods based on a smoothing-nonsmooth reformulation of nonsm...