Table of Contents
Preface
Author Contact Information
Chapter 1. The History of Newton’s Method and Extended Classical Results
Chapter 2. Extended Global Convergence of Iterative Methods
Chapter 3. Extended Gauss-Newton-Approximate Projection Methods of Constrained Nonlinear Least Squares Problems
Chapter 4. Convergence Analysis of Inexact Gauss-Newton Like for Solving Systems
Chapter 5. Local Convergence of the Gauss-Newton Scheme on Hilbert Spaces Under a Restricted Convergence Domain
Chapter 6. Ball Convergence for Inexact Newton-type Conditional Gradient Solver for Constrained Systems
Chapter 7. Newton-like Methods with Recursive Approximate Inverses
Chapter 8. Updated Mesh Independence Principle
Chapter 9. Ball Convergence for Ten Solvers Under the Same Set of Conditions
Chapter 10. Extended Newton’s Solver for Generalized Equations Using a Restricted Convergence Domain
Chapter 11. Extended Newton’s Method for Solving Generalized Equations: Kantorovich’s Approach
Chapter 12. Extended Robust Convergence Analysis of Newton’s Method for Cone Inclusion Problems in Banach Spaces
Chapter 13. Extended and Robust Kantorovich’s Theorem on the Inexact Newton’s Method with Relative Residual Error Tolerance
Chapter 14. Extended Local Convergence for Iterative Schemes Using the Gauge Function Theory
Chapter 15. Improved Local Convergence of Inexact Newton Methods under Average Lipschitz-type Conditions
Chapter 16. Semi-Local Convergence of Newton’s Method Using the Gauge Function Theory: An Extension
Chapter 17. Extending the Semi-Local Convergence of Newton’s Method Using the Gauge Theory
Chapter 18. Global Convergence for Chebyshev’s Method
Chapter 19. Extended Convergence of Efficient King-Werner-Type Methods of Order 1+√2
Chapter 20. Extended Convergence for Two Chebyshev-Like Methods
Chapter 21. Extended Convergence Theory for Newton-Like Methods of Bounded Deterioration
Chapter 22. Extending the Kantorovich Theorem for Solving Equations Using Telescopic Series
Chapter 23. Extended ω-Convergence Conditions for the Newton-Kantorovich Method
Chapter 24. Extended Semilocal Convergence Analysis for Directional Newton Method
Chapter 25. Extended Convergence of Damped Newton’s Method
Chapter 26. Extended Convergence Analysis of a One-Step Intermediate Newton Iterative Scheme for Nonlinear Equations
Chapter 27. Enlarging the Convergence Domain of Secant-Type Methods
Chapter 28. Two-Step Newton-Type Method for Solving Equations
Chapter 29. Two-Step Secant-Type Method for Solving Equations
Chapter 30. Unified Convergence for General Iterative Schemes
Chapter 31. Extending the Applicability of Gauss-Newton Method for Convex Composite Optimization
Chapter 32. Local Convergence Comparison Between Newton’s and the Secant Method: Part-I
Chapter 33. Convergence Comparison Between Newton’s and Secant Method: Part-II
Chapter 34. Extended Convergence Domains for a Certain Class of Fredholm Hammerstein Equations
Chapter 35. Extended Convergence of the Gauss-Newton-Kurchatov Method
Chapter 36. Extended Semi-Local Convergence of Newton’s Method under Conditions on the Second Derivative
Chapter 37. Extended Convergence for the Secant Method Under Mysovskii-like Conditions
Glossary of Symbols
