Iterative Algorithms 2

In this monograph, we present the complete recent work of the past decade of the authors on convergence and applications of iterative methods. It is the natural outgrowth of their related publications in these areas. Chapters are self-contained and can be read independently. Moreover, an extensive list of references is given in each chapter, in order to allow reader to use the previous ideas. For these reasons, we think that several advanced courses can be taught using this book.

The list of presented topic of our related studies follows:

• Convergence of Halley’s method under centered Lipschitz condition on the second Frechet derivative;
• Semilocal convergence of Steffensen-type algorithms;
• Some weaker extensions of the Kantorovich theorem for solving equations;
• Improved convergence analysis of Newton’s method;
• Extending the applicability of Newton’s method;
• Extending the applicability of Newton’s method for sections on Riemannian mani-folds;
• Two-step Newton methods;
• Discretized Newton-Tikhonov Method;
• Relaxed secant-type methods;
• Newton-Kantorovich method for analytic operators;
• Iterative Regularization methods for ill-posed Hammerstein type Operator Equations;
• Local convergence of a fifth order Method in Banach space;
• Local convergence of the Gauss-Newton method;
• Expanding the applicability of the Gauss-Newton method for convex optimization under a majorant condition;
• An Analysis of Lavrentiev Regularization Methods and Newton-type Iterative methods for Nonlinear Ill-posed Hammerstein-type Equations;
• Local Convergence of a multi-point-parameter Newton-like methods in Banach space;
• On an iterative method for unconstrained optimization;
• Inexact two-point Newton-like methods under general conditions.

The book’s results are expected to find applications in many areas of applied mathematics, engineering, computer science and real problems. As such this monograph is suitable to researchers, graduate students and seminars in the above subjects, also to be in all science and engineering libraries.

Table of Contents

Chapter 1 Convergence Of Halley’S Method Under Centered Lipschitz Condition On The Second Fr´Echet 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 Method
Chapter 5 Extending The Applicability Of Newton’S Method
Chapter 6 Extending The Applicability Of Newton’S Method For Sections On 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 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 Regularizationmethods 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 Iterativemethod For Unconstrained Optimization
Chapter 18 Inexact Two-Point Newton-Like Methods Under General Conditions