The preperiodic dynatomic curve is the closure in ℂ² of the set of (c,z) such that z is a preperiodic point of the polynomial with preperiod n and period p (n,p ≥ 1). We prove that each has exactly d-1 irreducible components, which are all smooth and have pairwise transverse intersections at the singular points of . We also compute the genus of each component and the Galois group of the defining polynomial of .
The paper is devoted to two systems of nonsmooth equations. One is the system of equations of max-type functions and the other is the system of equations of smooth compositions of max-type functions. The Newton and approximate Newton methods for these two systems are proposed. The Q-superlinear convergence of the Newton methods and the Q-linear convergence of the approximate Newton methods are established. The present methods can be more easily implemented than the previous ones, since they do not...
In this paper, we present a simultaneous subgradient algorithm for solving the multiple-sets split feasibility problem. The algorithm employs two extrapolated factors in each iteration, which not only improves feasibility by eliminating the need to compute the Lipschitz constant, but also enhances flexibility due to applying variable step size. The convergence of the algorithm is proved under suitable conditions. Numerical results illustrate that the new algorithm has better convergence than the...
An equivalent model of nonsmooth equations for a constrained minimax problem is derived by using a KKT optimality condition. The Newton method is applied to solving this system of nonsmooth equations. To perform the Newton method, the computation of an element of the -differential for the corresponding function is developed.
In this paper, we discuss the globalization of some kind of modified Levenberg-Marquardt methods for nonsmooth equations and their applications to nonlinear complementarity problems. In these modified Levenberg-Marquardt methods, only an approximate solution of a linear system at each iteration is required. Under some mild assumptions, the global convergence is shown. Finally, numerical results show that the present methods are promising.
In this paper we propose a parametrized Newton method for nonsmooth equations with finitely many maximum functions. The convergence result of this method is proved and numerical experiments are listed.
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