On Newton-like iteration functions: General convergence theorems and a specific algorithm

Convergence of Newton { like

We present a (semilocal) Kantorovich{type analysis for Newton{like methods for singular operator equations using outer inverses. We establish sharp generalizations of the Kantorovich theory and the Mysovskii theory for operator equations when the derivative is not necessarily invertible. The results reduce in the case of an invertible derivative to well{known theorems of Kantorovich and Mysovsk...

Note on fast division algorithm for polynomials using Newton iteration

The classical division algorithm for polynomials requires O(n) operations for inputs of size n. Using reversal technique and Newton iteration, it can be improved to O(M(n)), where M is a multiplication time. But the method requires that the degree of the modulo, x, should be the power of 2. If l is not a power of 2 and f(0) = 1, Gathen and Gerhard suggest to compute the inverse, f, modulo x r⌉,...

On Fast Division Algorithm for Polynomials Using Newton Iteration

Convergence of the multistage variational iteration method for solving a general system of ordinary differential equations

In this paper, the multistage variational iteration method is implemented to solve a general form of the system of first-order differential equations. The convergence of the proposed method is given. To illustrate the proposed method, it is applied to a model for HIV infection of CD4+ T cells and the numerical results are compared with those of a recently proposed method.

Network Newton–Part I: Algorithm and Convergence

We study the problem of minimizing a sum of convex objective functions where the components of the objective are available at different nodes of a network and nodes are allowed to only communicate with their neighbors. The use of distributed gradient methods is a common approach to solve this problem. Their popularity notwithstanding, these methods exhibit slow convergence and a consequent larg...