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Iterative Methods and Their Dynamics with Applications : a Contemporary Study.

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Iterative processes are the tools used to generate sequences approximating solutions of equations describing real life problems. Intended for researchers in computational sciences and as a reference book for advanced computational method in nonlinear analysis, this book is a collection of the recent...

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Bibliographic Details
Main Author: Argyros, Ioannis Konstantinos
Corporate Author: Taylor & Francis
Other Authors: Magreñán, Á. Alberto (Ángel Alberto)
Format: eBook
Language:English
Published: Portland : CRC Press, 2017.
Subjects:
Iterative methods (Mathematics)
Itération (Mathématiques)
MATHEMATICS > Differential Equations.
MATHEMATICS > Number Systems.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Cover
  • Half title
  • Title
  • Copyright
  • Dedication
  • Preface
  • Contents
  • List of Figures
  • List of Tables
  • Symbol Description
  • Chapter 1 Halley's method
  • 1.1 Introduction
  • 1.2 Semilocal convergence of Halley's method
  • 1.3 Numerical examples
  • 1.4 Basins of attraction
  • 1.4.1 2 roots
  • 1.4.2 3 roots
  • 1.4.3 4 roots
  • References
  • Chapter 2 Newton's method for k-Fréchet differentiable operators
  • 2.1 Introduction
  • 2.2 Semilocal convergence analysis for Newton's method
  • 2.2.1 Uniqueness of solution
  • 2.2.2 Special choices for function g
  • 2.2.2.1 Choice 1
  • 2.2.2.2 Choice 2
  • 2.3 Numerical examples
  • References
  • Chapter 3 Nonlinear Ill-posed equations
  • 3.1 Introduction
  • 3.2 Convergence analysis
  • 3.3 Error bounds
  • 3.4 Implementation of adaptive choice rule
  • 3.4.1 Algorithm
  • 3.5 Numerical examples
  • References
  • Chapter 4 Sixth-order iterative methods
  • 4.1 Introduction
  • 4.2 Scheme for constructing sixth-order iterative methods
  • 4.3 Sixth-order iterative methods contained in family USS
  • 4.4 Numerical work
  • 4.4.1 Solving nonlinear equations
  • 4.5 Dynamics for method SG
  • 4.5.1 Study of the fixed points and their stability
  • 4.5.2 Study of the critical points and parameter spaces
  • References
  • Chapter 5 Local convergence and basins of attraction of a two-step Newton-like method for equations with solutions of multiplicity greater than one
  • 5.1 Introduction
  • 5.2 Local convergence
  • 5.3 Basins of attraction
  • 5.3.1 Basins of F(x) = (x
  • 1)2(x + 1)
  • 5.3.2 Basins of F(x) = (x
  • 1)3(x + 1)
  • 5.3.3 Basins of F(x) = (x
  • 1)4(x + 1)
  • 5.4 Numerical examples
  • References
  • Chapter 6 Extending the Kantorovich theory for solving equations
  • 6.1 Introduction
  • 6.2 First convergence improvement
  • 6.3 Second convergence improvement
  • References.
  • Chapter 7 Robust convergence for inexact Newton method
  • 7.1 Introduction
  • 7.2 Standard results on convex functions
  • 7.3 Semilocal convergence
  • 7.4 Special cases and applications
  • References
  • Chapter 8 Inexact Gauss-Newton-like method for least square problems
  • 8.1 Introduction
  • 8.2 Auxiliary results
  • 8.3 Local convergence analysis
  • 8.4 Applications and examples
  • References
  • Chapter 9 Lavrentiev Regularization methods for Ill-posed equations
  • 9.1 Introduction
  • 9.2 Basic assumptions and some preliminary results
  • 9.3 Error estimates
  • 9.3.1 Apriori parameter choice
  • 9.3.2 Aposteriori parameter choice
  • 9.4 Numerical examples
  • References
  • Chapter 10 King-Werner-type methods of order 1 + 2
  • 10.1 Introduction
  • 10.2 Majorizing sequences for King-Werner-type methods
  • 10.3 Convergence analysis of King-Werner-type methods
  • 10.4 Numerical examples
  • References
  • Chapter 11 Generalized equations and Newton's method
  • 11.1 Introduction
  • 11.2 Preliminaries
  • 11.3 Semilocal convergence
  • References
  • Chapter 12 Newton's method for generalized equations using restricted domains
  • 12.1 Introduction
  • 12.2 Preliminaries
  • 12.3 Local convergence
  • 12.4 Special cases
  • References
  • Chapter 13 Secant-like methods
  • 13.1 Introduction
  • 13.2 Semilocal convergence analysis of the secant method I
  • 13.3 Semilocal convergence analysis of the secant method II
  • 13.4 Local convergence analysis of the secant method I
  • 13.5 Local convergence analysis of the secant method II
  • 13.6 Numerical examples
  • References
  • Chapter 14 King-Werner-like methods free of derivatives
  • 14.1 Introduction
  • 14.2 Semilocal convergence
  • 14.3 Local convergence
  • 14.4 Numerical examples
  • References
  • Chapter 15 M uller's method
  • 15.1 Introduction
  • 15.2 Convergence ball for method (15.1.2)
  • 15.3 Numerical examples.