Advances in Iterative Methods for Nonlinear Equations

Editors: Sergio Amat, Sonia Busquier



Provides an overview on the construction and selection of iterative methods

Addresses both numerical and theoretical analysis of iterative methods

Features accompanying tables and figures

This book focuses on the approximation of nonlinear equations using iterative methods. Nine contributions are presented on the construction and analysis of these methods, the coverage encompassing convergence, efficiency, robustness, dynamics, and applications. Many problems are stated in the form of nonlinear equations, using mathematical modeling. In particular, a wide range of problems in Applied Mathematics and in Engineering can be solved by finding the solutions to these equations. The book reveals the importance of studying convergence aspects in iterative methods and shows that selection of the most efficient and robust iterative method for a given problem is crucial to guaranteeing a good approximation. A number of sample criteria for selecting the optimal method are presented, including those regarding the order of convergence, the computational cost, and the stability, including the dynamics. This book will appeal to researchers whose field of interest is related to nonlinear problems and equations, and their approximation.   

Table of contents

Front Matter
Pages i-v

Introduction
Pages 1-3

An Overview on Steffensen-Type Methods
Pages 5-21

Newton’s Method for Convex Optimization
Pages 23-56

Inexact Newton Methods on Riemannian Manifolds
Pages 57-78

On the Design of Optimal Iterative Methods for Solving Nonlinear Equations
Pages 79-111

The Theory of Kantorovich for Newton’s Method: Conditions on the Second Derivative
Pages 113-145

Complexity of an Homotopy Method at the Neighbourhood of a Zero
Pages 147-171

A Qualitative Analysis of a Family of Newton-Like Iterative Process with R-Order of Convergence At Least Three
Pages 173-210

Measures of the Basins of Attracting n-Cycles for the Relaxed Newton’s Method
Pages 211-245

On Convergence and Efficiency in the Resolution of Systems of Nonlinear Equations from a Local Analysis
Pages 247-286

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