Iterative Algorithms II

Ioannis K. Argyros
Cameron University, Department of Mathematical Sciences, Lawton, OK, USA

Á. Alberto Magreñán
Universidad Internacional de La Rioja, Departamento de Matemáticas, La Rioja, Spain

Series: Mathematics Research Developments
BISAC: MAT003000

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The study of iterative methods began several years ago in order to find the solutions of problems where mathematicians cannot find a solution in closed form. In this way, different studies related to different methods with different behaviors have been presented over the last decades.

Convergence conditions have become one of the most studied topics in recent mathematical research. One of the most well-known conditions are the Kantorovich conditions, which has allowed many researchers to experiment with all kinds of conditions. In recent years, several authors have studied different modifications of the mentioned conditions considering inter alia, Hölder conditions, alpha-conditions or even convergence in other spaces.

In this monograph, the authors present the complete work within the past decade on convergence and dynamics of iterative methods. It acts as an extension of their related publications in these areas. The chapters are self-contained and can be read independently. Moreover, an extensive list of references is given in each chapter, in order to allow the reader to refer to previous ideas. For these reasons, several advanced courses can be taught using this book.
This book intends to find applications in many areas of applied mathematics, engineering, computer science and real problems. As such, this monograph is suitable for researchers, graduate students and seminars in the above subjects, and it would be an excellent addition to all science and engineering libraries. (Imprint: Nova)

Dedication

Preface

Chapter 1. Convergence of Halley's Method Under Centered Lipschitz Condition on the Second Fréchet Derivative

Chapter 2. Semilocal Convergence of Steffensen-type Algorithms

Chapter 3. Some Weaker Extensions of the Kantorovich Theorem for Solving Equations

Chapter 4. Improved Convergence Analysis of Newton's Methods

Chapter 5. Extending the Applicability of Newton's Method

Chapter 6. Extending the Applicability of Newton's Method for Sections in Riemannian Manifolds

Chapter 7. Two-step Newton Methods

Chapter 8. Discretized Newton-Tikhonov Method

Chapter 9. Relaxed Secant-type Methods

Chapter 10. Newton-Kantorovich Method for Analytic Operators

Chapter 11. Iterative Regularization Methods for Ill-posed Hammerstein Type Operator Equations

Chapter 12. Local Convergence of a Fifth Order Method in Banach Space

Chapter 13. Local Convergence of the Gauss-Newton Method

Chapter 14. Expanding the Applicability of the Gauss-Newton Method for Convex Optimization Under a Majorant Condition

Chapter 15. An Analysis of Lavrentiev Regularization Methods and Newton-type Iterative Methods for Nonlinear Ill-posed Hammerstein-type Equations

Chapter 16. Local Convergence of a Multi-point-parameter Newton-like Methods in Banach Space

Chapter 17. On an Iterative Method for Unconstrained Optimization

Chapter 18. Inexact two-point Newton-like Methods Under General Conditions

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