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Advances in Iterative Methods for Nonlinear Equations

  • Book
  • © 2016

Overview

Editors:
  1. Sergio Amat

    1. Departamento de Matemática, Aplicada y Estadística Universidad Politécnica de Cartagena, Cartagena, Spain

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  2. Sonia Busquier

    1. Departamento de Matemática, Aplicada y Estadística Universidad Politécnica de Cartagena, Cartagena, Spain

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  • 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
  • Includes supplementary material: sn.pub/extras

Part of the book series: SEMA SIMAI Springer Series (SEMA SIMAI, volume 10)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-v
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  2. Introduction

    • Sergio Amat
    Pages 1-3

  3. An Overview on Steffensen-Type Methods

    • S. Amat, S. Busquier, Á. A. Magreñán, L. Orcos
    Pages 5-21

  4. Newton’s Method for Convex Optimization

    • Ioannis K. Argyros, Daniel González
    Pages 23-56

  5. Inexact Newton Methods on Riemannian Manifolds

    • I. K. Argyros, Á. A. Magreñán
    Pages 57-78

  6. On the Design of Optimal Iterative Methods for Solving Nonlinear Equations

    • Alicia Cordero, Juan R. Torregrosa
    Pages 79-111

  7. The Theory of Kantorovich for Newton’s Method: Conditions on the Second Derivative

    • J. A. Ezquerro, M. A. Hernández-Verón
    Pages 113-145

  8. Complexity of an Homotopy Method at the Neighbourhood of a Zero

    • J.-C. Yakoubsohn, J. M. Gutiérrez, Á. A. Magreñán
    Pages 147-171

  9. A Qualitative Analysis of a Family of Newton-Like Iterative Process with R-Order of Convergence At Least Three

    • M. A. Hernández-Verón, N. Romero
    Pages 173-210

  10. Measures of the Basins of Attracting n-Cycles for the Relaxed Newton’s Method

    • J. M. Gutiérrez, L. J. Hernández, Á. A. Magreñán, M. T. Rivas
    Pages 211-245

  11. On Convergence and Efficiency in the Resolution of Systems of Nonlinear Equations from a Local Analysis

    • Miquel Grau-Sánchez, Miquel Noguera
    Pages 247-286
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Keywords

About this book

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.   

Editors and Affiliations

  • Departamento de Matemática, Aplicada y Estadística Universidad Politécnica de Cartagena, Cartagena, Spain

    Sergio Amat, Sonia Busquier

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