The Theory and Applications of Iteration Methods

Cover
Half Title
Title Page
Copyright Page
Dedication
	Contents
Preface
Acknowledgement
Author
Chapter 1: The Convergence of Algorithmic Models
	1.1. Algorithmic Models
	1.2. Convergence Criteria for Algorithmic Models
	1.3. Applications
	1.4. Exercises
	References
Chapter 2: The Convergence of Iteration Sequences
	2.1. The General Convergence Theorem
	2.2. Convergence of l-Step Methods
	2.3. Convergence of Single-Step Methods
	2.4. Convergence of Single-Step Methods with Differentiable Iteration Functions
	2.5. Applications
	2.6. Exercises
	References
Chapter 3: Monotone Convergence
	3.1. General Results
	3.2. A General Model in Linear Spaces
	3.3. Applications
	3.4. Exercises
	References
Chapter 4: Applications in:
	4.1. Neural Networks
	4.2. Reliability Engineering
	4.3. Economic Models
	4.4. Exercises
	References
Chapter 5: A Novel Scheme Free from Derivatives
	5.1. Convergence
	5.2. Applications
	5.3. Exercises
	References
Chapter 6: Efficient Sixth Convergence Order Method
	6.1. Local convergence
	6.2. Applications
	6.3. Exercises
	References
Chapter 7: High-Order Iterative Methods
	7.1. Local convergence Analysis I
	7.2. Local convergence analysis II
	7.3. Applications
	7.4. Applications with large systems
	7.5. Exercises
	References
Chapter 8: Unified Local Convergence of k–Step Solvers
	8.1. Local Convergence
	8.2. Applications
	8.3. Exercises
	References
Chapter 9: Ball Comparison Between Three Sixth-Order Methods
	9.1. Local Convergence
	9.2. Applications
	9.3. Exercises
	References
Chapter 10: Constrained Generalized Equations
	10.1. Notation and auxiliary results
	10.2. The local Newton method
	10.3. Applications
	10.4. Exercises
	References
Chapter 11: Inexact Gauss–Newton Method for Solving Least Squares Problems
	11.1. Majorizing sequences
	11.2. Convergence Analysis for Algorithm TGNU (I)
	11.3. Convergence Analysis for Algorithm TGNU (II)
	11.4. Applications
	11.5. Exercises
	References
Chapter 12: The Kantorovich’s Theorem on Newton’s Method for Solving Generalized Equation
	12.1. Preliminaries
	12.2. Kantorovich’s theorem for Newton’s method
	12.3. Applications
	12.4. Exercises
	References
Chapter 13: An Inverse Free Broyden’s Method
	13.1. Preliminaries: regularly continuous dd
	13.2. Semi-local convergence analysis of BM
	13.3. Applications
	13.4. Exercises
	References
Chapter 14: Complexity of a Homotopy Method for Locating an Approximate Zero
	14.1. Convergence analysis
	14.2. Special Cases
	14.3. Applications
	14.4. Exercises
	References
Chapter 15: Inexact Methods for Finding Zeros with Multiplicity
	15.1. Auxiliary results
	15.2. Ball convergence
	15.3. Applications
	15.4. Exercises
	References
Chapter 16: Multi-Step High Convergence Order Methods
	16.1. Local convergence analysis
	16.2. Applications
	16.3. Exercises
	References
Chapter 17: Two-Step Gauss-Newton Werner-Type Method for Least Squares Problems
	17.1. Local convergence analysis
	17.2. Applications
	17.3. Exercises
	References
Chapter 18: Convergence for m–Step Iterative Methods
	18.1. Semi-local convergence
	18.2. Applications
	18.3. Exercises
	References
Chapter 19: Convergence of Newton’s Method on Lie Groups
	19.1. Background
	19.2. Semi-local convergence
	19.3. Exercises
	References
Chapter 20: The Convergence Region of m-Step Iterative Procedures
	20.1. Semi-local Convergence
	20.2. Applications
	20.3. Exercises
	References
Chapter 21: Efficient Eighth Order Method in Banach Spaces Under Weak w–Conditions
	21.1. Local convergence
	21.2. Semi-local convergence
	21.3. Applications
	21.4. Exercises
	References
Chapter 22: Schröder-Like Methods for Multiple Roots
	22.1. Ball convergence
	22.2. Exercises
	References
Chapter 23: Gauss-Newton Solver for Systems of Equations
	23.1. Ball convergence
	23.2. Exercises
	References
Chapter 24: High-Order Iterative Schemes Under Kantorovich Hypotheses
	24.1. Semi-local Convergence
	24.2. Applications
	24.3. Exercises
	References
Chapter 25: Semi-Local Convergence of a Derivative Free Method
	25.1. Semi-local convergence
	25.2. Applications
	25.3. Exercises
	References
Chapter 26: A new Higher-Order Iterative Scheme for the Solutions of Nonlinear Systems
	26.1. Multi-dimensional case
	26.2. Local convergence analysis
	26.3. Applications
	26.4. Exercises
	References
Glossary
Index