| Preface | p. vii |
| Divided Differences | p. 1 |
| Partially Ordered Topological Spaces | p. 1 |
| Divided Difference in a Linear Space | p. 4 |
| Divided Differences in a Banach Space | p. 5 |
| Divided Differences and Monotone Convergence | p. 11 |
| Divided Differences and Frechet-derivatives | p. 16 |
| Exercises | p. 21 |
| Constants and Functions Appearing in Numerical Methods | p. 29 |
| Preliminaries | p. 29 |
| Lipschitz Conditions and Norm Estimate | p. 34 |
| Lipschitz Conditions for Uryson Operators | p. 36 |
| The Case X = C | p. 39 |
| The Case X = L[infinity] | p. 41 |
| The Case X = Lp, 1 [left than or equal] p [left than or equal] 2 | p. 43 |
| The Case X = Lp, 2 [ p [ [infinity] | p. 44 |
| Exercises | p. 46 |
| Convergence and Error Analysis for Iterative Methods | p. 57 |
| Preliminaries | p. 59 |
| A Unified Approach for Constructing Inexact Newton-Like Methods | p. 61 |
| Semilocal Convergence Results for Newton-Like Methods | p. 80 |
| A Fixed Point Proof for Extended Newton-Like Methods | p. 90 |
| A Generalization of Edelstein's Theorem on Fixed Points | p. 97 |
| Weak Conditions for the Convergence of Iterations | p. 102 |
| Monotone Convergence of Implicit Newton-Like Methods | p. 108 |
| General Ways of Constructing Accelerating Newton-Like Iterations | p. 113 |
| A Generalization of Ostrowski's Theorem on Fixed Points | p. 117 |
| Exercises | p. 120 |
| Special Topics | p. 155 |
| Convergence Rates for Inexact Newton-Like Methods at Singular Points | p. 155 |
| Smoothness and Inexact Newton-Like Methods | p. 171 |
| Convergence Domains Using Outer or Generalized Inverses | p. 185 |
| Exercises | p. 203 |
| Convergence in Generalized Banach Spaces | p. 207 |
| Convergence of Inexact Newton-Like Methods with a Convergence Structure | p. 207 |
| Improving the Rate of Convergence | p. 218 |
| Controlling the Residuals of Inexact Newton-Like Methods | p. 222 |
| Exercises | p. 231 |
| Discretization of Newton-Like Methods | p. 247 |
| The Mesh Independence Principle for Inexact Newton-Like Methods | p. 247 |
| A New Newton--Mysovskii-Type Theorem | p. 275 |
| Inexact Newton--Galerkin-Like Methods | p. 296 |
| Exercises | p. 317 |
| Convergence Analysis Based on the Second Frechet-Derivative | p. 323 |
| A New Convergence Theorem Based on the Second Frechet-Derivative | p. 323 |
| Improved Error Bounds | p. 331 |
| A New Kantorovich-Type Theorem Involving First and Second Derivatives | p. 340 |
| Newton-Like Methods Using Twice Frechet Differentiable Operators | p. 347 |
| The Convergence of Newton's Method for Polynomial Equations | p. 356 |
| Uniform-Like Continuity Conditions | p. 368 |
| A Global Convergence Theorem | p. 376 |
| Semilocal Convergence Theorems | p. 381 |
| Semilocal Convergence Theorems II | p. 390 |
| Local Convergence Theorems | p. 397 |
| Monotone Convergence and Divided Differences of Order Two | p. 406 |
| Exercises | p. 412 |
| Forcing Sequences and the Second Frechet-Derivative | p. 419 |
| Relations Between Forcing Sequences and Inexact Newton Iterates | p. 419 |
| Affine Invariant Local Convergence Theorems for Inexact Newton-Like Methods | p. 432 |
| The Radius of Convergence of Newton's Method | p. 444 |
| Local Convergence Involving the Second Frechet-Derivative | p. 455 |
| Choosing Forcing Sequences | p. 463 |
| Rounding Errors | p. 472 |
| Convergence and Residuals | p. 478 |
| Relations Between Forcing Sequences and Inexact Newton-Like Iterates | p. 487 |
| Exercises | p. 495 |
| Numerical Algorithms | p. 503 |
| References | p. 527 |
| Glossary of Symbols | p. 543 |
| Index | p. 545 |
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