A Contemporary Study of Iterative Methods: Convergence, Dynamics and Applications evaluates and compares advances in iterative techniques, also discussing their numerous applications in applied mathematics, engineering, mathematical economics, mathematical biology and other applied sciences. It uses the popular iteration technique in generating the approximate solutions of complex nonlinear equations that is suitable for aiding in the solution of advanced problems in engineering, mathematical economics, mathematical biology and other applied sciences. Iteration methods are also applied for solving optimization problems. In such cases, the iteration sequences converge to an optimal solution of the problem at hand.
The majorization method in the Kantorovich theory Directional Newton methods Newton's method Generalized equations Gauss-Newton method Gauss-Newton method for convex optimization Proximal Gauss-Newton method Multistep modified Newton-Hermitian and Skew-Hermitian Splitting method Secant-like methods in chemistry Robust convergence of Newton's method for cone inclusion problem Gauss-Newton method for convex composite optimization Domain of parameters Newton's method for solving optimal shape design problems Osada method Newton's method to solve equations with solutions of multiplicity greater than one Laguerre-like method for multiple zeros Traub's method for multiple roots Shadowing lemma for operators with chaotic behavior Inexact two-point Newton-like methods Two-step Newton methods Introduction to complex dynamics Convergence and the dynamics of Chebyshev-Halley type methods Convergence planes of iterative methods Convergence and dynamics of a higher order family of iterative methods Convergence and dynamics of iterative methods for multiple zeros