Methods for Solving Systems of Nonlinear Equations
2nd Edition
Published on 30. September 1998
Book
Paperback/Softback
157 pages
978-0-89871-415-9 (ISBN)
Description
This second edition provides much-needed updates to the original volume. Like the first edition, it emphasizes the ideas behind the algorithms as well as their theoretical foundations and properties, rather than focusing strictly on computational details; at the same time, this new version is now largely self-contained and includes essential proofs.
Additions have been made to almost every chapter, including an introduction to the theory of inexact Newton methods, a basic theory of continuation methods in the setting of differentiable manifolds, and an expanded discussion of minimization methods. New information on parametrized equations and continuation incorporates research since the first edition.
Additions have been made to almost every chapter, including an introduction to the theory of inexact Newton methods, a basic theory of continuation methods in the setting of differentiable manifolds, and an expanded discussion of minimization methods. New information on parametrized equations and continuation incorporates research since the first edition.
More details
Series
Edition
Second Edition
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Edition type
New edition
Product notice
Paperback (trade)
Unsewn / adhesive bound
Dimensions
Height: 228 mm
Width: 152 mm
Thickness: 10 mm
Weight
299 gr
ISBN-13
978-0-89871-415-9 (9780898714159)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Previous edition
Werner C. Rheinboldt
Methods for Solving Systems of Nonlinear Equations
Book
02/1987
Society for Industrial & Applied Mathematics,U.S.
€43.46
Article exhausted; check for reprint
Content
Preface to the Second Edition
Preface to the First Edition
Chapter 1: Introduction. Problem Overview
Notation and Background
Chapter 2: Model Problems. Discretization of Operator Equations
Minimization
Discrete Problems
Chapter 3: Iterative Processes and Rates of Convergence. Characterization of Iterative Processes
Rates of Convergence
Evaluation of Convergence Rates
On Efficiency and Accuracy
Chapter 4: Methods of Newton Type. The Linearization Concept
Methods of Newton Form
Discretized Newton Methods
Attraction Basins
Chapter 5: Methods of Secant Type. General Secant Methods
Consistent Approximations
Update Methods
Chapter 6: Combinations of Processes. The Use of Classical Linear Methods
Nonlinear SOR Methods
Residual Convergence Controls
Inexact Newton Methods
Chapter 7: Parametrized Systems of Equations. Submanifolds of R n
Continuation Using ODEs
Continuation with Local Parametrizations
Simplicial Approximations of Manifolds
Chapter 8: Unconstrained Minimization Methods. Admissible Step Length Algorithms
Gradient Related Methods
Collectively Gradient Related Directions
Trust Region Methods
Chapter 9: Nonlinear Generalizations of Several Matrix Classes. Basic Function Classes
Properties of the Function Classes
Convergence of Iterative Processes
Chapter 10: Outlook at Further Methods. Higher Order Methods
Piecewise-Linear Methods
Further Minimization Methods
Bibliography
Index.
Preface to the First Edition
Chapter 1: Introduction. Problem Overview
Notation and Background
Chapter 2: Model Problems. Discretization of Operator Equations
Minimization
Discrete Problems
Chapter 3: Iterative Processes and Rates of Convergence. Characterization of Iterative Processes
Rates of Convergence
Evaluation of Convergence Rates
On Efficiency and Accuracy
Chapter 4: Methods of Newton Type. The Linearization Concept
Methods of Newton Form
Discretized Newton Methods
Attraction Basins
Chapter 5: Methods of Secant Type. General Secant Methods
Consistent Approximations
Update Methods
Chapter 6: Combinations of Processes. The Use of Classical Linear Methods
Nonlinear SOR Methods
Residual Convergence Controls
Inexact Newton Methods
Chapter 7: Parametrized Systems of Equations. Submanifolds of R n
Continuation Using ODEs
Continuation with Local Parametrizations
Simplicial Approximations of Manifolds
Chapter 8: Unconstrained Minimization Methods. Admissible Step Length Algorithms
Gradient Related Methods
Collectively Gradient Related Directions
Trust Region Methods
Chapter 9: Nonlinear Generalizations of Several Matrix Classes. Basic Function Classes
Properties of the Function Classes
Convergence of Iterative Processes
Chapter 10: Outlook at Further Methods. Higher Order Methods
Piecewise-Linear Methods
Further Minimization Methods
Bibliography
Index.