Methods for solving systems of nonlinear equations /
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| Author / Creator: | Rheinboldt, Werner C. |
|---|---|
| Edition: | 2nd ed. |
| Imprint: | Philadelphia : Society for Industrial and Applied Mathematics, c1998. |
| Description: | ix, 148 p. ; 26 cm. |
| Language: | English |
| Series: | CBMS-NSF regional conference series in applied mathematics. 70 |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/3450905 |
Table of Contents:
- Preface to the Second Edition
- Preface to the First Edition
- Chapter 1.. Introduction
- 1.1. Problem Overview
- 1.2. Notation and Background
- Chapter 2.. Model Problems
- 2.1. Discretization of Operator Equations
- 2.2. Minimization
- 2.3. Discrete Problems
- Chapter 3.. Iterative Processes and Rates of Convergence
- 3.1. Characterization of Iterative Processes
- 3.2. Rates of Convergence
- 3.3. Evaluation of Convergence Rates
- 3.4. On Efficiency and Accuracy
- Chapter 4.. Methods of Newton Type
- 4.1. The Linearization Concept
- 4.2. Methods of Newton Form
- 4.3. Discretized Newton Methods
- 4.4. Attraction Basins
- Chapter 5.. Methods of Secant Type
- 5.1. General Secant Methods
- 5.2. Consistent Approximations
- 5.3. Update Methods
- Chapter 6.. Combinations of Processes
- 6.1. The Use of Classical Linear Methods
- 6.2. Nonlinear SOR Methods
- 6.3. Residual Convergence Controls
- 6.4. Inexact Newton Methods
- Chapter 7.. Parametrized Systems of Equations
- 7.1. Submanifolds of R[superscript n]
- 7.2. Continuation Using ODEs
- 7.3. Continuation with Local Parametrizations
- 7.4. Simplicial Approximations of Manifolds
- Chapter 8.. Unconstrained Minimization Methods
- 8.1. Admissible Step-Length Algorithms
- 8.2. Gradient-Related Methods
- 8.3. Collectively Gradient-Related Directions
- 8.4. Trust Region Methods
- Chapter 9.. Nonlinear Generalizations of Several Matrix Classes
- 9.1. Basic Function Classes
- 9.2. Properties of the Function Classes
- 9.3. Convergence of Iterative Processes
- Chapter 10.. Outlook at Further Methods
- 10.1. Higher-Order Methods
- 10.2. Piecewise-Linear Methods
- 10.3. Further Minimization Methods
- Bibliography
- Index
