Globally convergent homotopy algorithms for nonlinear systems of equations

A globally convergent Inexact-Newton method for solving reducible nonlinear systems of equations

A nonlinear system of equations is said to be reducible if it can be divided into m blocks (m > 1) in such a way that the i−th block depends only on the first i blocks of unknowns. Different ways of handling the different blocks with the aim of solving the system have been proposed in the literature. When the dimension of the blocks is very large, it can be difficult to solve the linear Newtoni...

Globally convergent techniques in nonlinear Newton-Krylov algorithms

Solving Systems of Nonlinear Equations Using a Globally Convergent Optimization Algorithm

Solving systems of nonlinear equations is a relatively complicated problem for which a number of different approaches have been presented. In this paper, a new algorithm is proposed for the solutions of systems of nonlinear equations. This algorithm uses a combination of the gradient and the Newton’s methods. A novel dynamic combinatory is developed to determine the contribution of the methods ...

Globally Convergent Newton Algorithms for Blind Decorrelation

This paper presents novel Newton algorithms for the blind adaptive decorrelation of real and complex processes. They are globally convergent and exhibit an interesting relationship with the natural gradient algorithm for blind decorrelation and the Goodall learning rule. Indeed, we show that these two later algorithms can be obtained from their Newton decorrelation versions when an exact matrix...

Homotopy Analysis Sumudu Transform Method for Nonlinear Equations