Advances in Iterative Methods for Nonlinear Equations

1. Front Matter

   Pages i-v

   PDF

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

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.   

• Iterative methods
• Convergence
• Efficiency
• Ergodic theory
• Computational mathematics

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

  Sergio Amat, Sonia Busquier

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