The theory and applications of iteration methods

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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