Interative Solution of Nonlinear Equations in Several Variables
Published on 31. March 2000
Book
Paperback/Softback
598 pages
978-0-89871-461-6 (ISBN)
Description
Provides a survey of the theoretical results on systems of nonlinear equations in finite dimension and the major iterative methods for their computational solution. Originally published in 1970, it offers a research-level presentation of the principal results known at that time.
Although the field has developed since the book originally appeared, it remains a major background reference for the literature before 1970. In particular, Part II contains the only relatively complete introduction to the existence theory for finite-dimensional nonlinear equations from the viewpoint of computational mathematics. Over the years semilocal convergence results have been obtained for various methods, especially with an emphasis on error bounds for the iterates. The results and proof techniques introduced here still represent a solid basis for this topic.
Although the field has developed since the book originally appeared, it remains a major background reference for the literature before 1970. In particular, Part II contains the only relatively complete introduction to the existence theory for finite-dimensional nonlinear equations from the viewpoint of computational mathematics. Over the years semilocal convergence results have been obtained for various methods, especially with an emphasis on error bounds for the iterates. The results and proof techniques introduced here still represent a solid basis for this topic.
More details
Series
Edition
Revised edition
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Edition type
Annotated edition
Product notice
Paperback (trade)
Unsewn / adhesive bound
Dimensions
Height: 230 mm
Width: 154 mm
Thickness: 28 mm
Weight
816 gr
ISBN-13
978-0-89871-461-6 (9780898714616)
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
Content
Preface to the Classics Edition
Preface
Acknowledgments
Glossary of Symbols
Introduction
Part I: Background Material. Chapter 1: Sample Problems
Chapter 2: Linear Algebra
Chapter 3: Analysis
Part II: Nonconstructive Existence Theorems. Chapter 4: Gradient Mappings and Minimization
Chapter 5: Contractions and the Continuation Property
Chapter 6: The Degree of a Mapping
Part III: Iterative Methods. Chapter 7: General Iterative Methods
Chapter 8: Minimization Methods
Part IV: Local Convergence. Chapter 9: Rates of Convergence?General
Chapter 10: One-Step Stationary Methods
Chapter 11: Multistep Methods and Additional One-Step Methods
Part V: Semilocal and Global Convergence. Chapter 12: Contractions and Nonlinear Majorants
Chapter 13: Convergence under Partial Ordering
Chapter 14: Convergence of Minimization Methods
An Annotated List of Basic Reference Books
Bibliography
Author Index
Subject Index.
Preface
Acknowledgments
Glossary of Symbols
Introduction
Part I: Background Material. Chapter 1: Sample Problems
Chapter 2: Linear Algebra
Chapter 3: Analysis
Part II: Nonconstructive Existence Theorems. Chapter 4: Gradient Mappings and Minimization
Chapter 5: Contractions and the Continuation Property
Chapter 6: The Degree of a Mapping
Part III: Iterative Methods. Chapter 7: General Iterative Methods
Chapter 8: Minimization Methods
Part IV: Local Convergence. Chapter 9: Rates of Convergence?General
Chapter 10: One-Step Stationary Methods
Chapter 11: Multistep Methods and Additional One-Step Methods
Part V: Semilocal and Global Convergence. Chapter 12: Contractions and Nonlinear Majorants
Chapter 13: Convergence under Partial Ordering
Chapter 14: Convergence of Minimization Methods
An Annotated List of Basic Reference Books
Bibliography
Author Index
Subject Index.