Iterative Methods for Solving Nonlinear Equations and Systems

Solving nonlinear equations in any Banach space (real or complex nonlinear equations, nonlinear systems, and nonlinear matrix equations, among others) is a non-trivial task that involves many areas of science and technology. Usually the solution is not directly affordable and requires an approach utilizing iterative algorithms. This is an area of research that has grown exponentially over the last few years.
This Special Issue focuses mainly on the design, analysis of convergence, and stability of new iterative schemes for solving nonlinear problems and their application to practical problems. Included papers study the following topics: Methods for finding simple or multiple roots, either with or without derivatives, iterative methods for approximating different generalized inverses, and real or complex dynamics associated with the rational functions resulting from the application of an iterative method on a polynomial function. Additionally, the analysis of the convergence of the proposed methods has been carried out by means of different sufficient conditions assuring the local, semilocal, or global convergence.
This Special issue has allowed us to present the latest research results in the area of iterative processes for solving nonlinear equations as well as systems and matrix equations. In addition to the theoretical papers, several manuscripts on signal processing, nonlinear integral equations, partial differential equations, or convex programming reveal the connection between iterative methods and other branches of science and engineering.