Newton Methods for Nonlinear Problems
Affine Invariance and Adaptive Algorithms
Published on 18. September 2011
XII, 424 pages
978-3-642-23899-4 (ISBN)
Description
This book deals with the efficient numerical solution of challenging nonlinear problems in science and engineering, both in finite dimension (algebraic systems) and in infinite dimension (ordinary and partial differential equations). Its focus is on local and global Newton methods for direct problems or Gauss-Newton methods for inverse problems. The term 'affine invariance' means that the presented algorithms and their convergence analysis are invariant under one out of four subclasses of affine transformations of the problem to be solved. Compared to traditional textbooks, the distinguishing affine invariance approach leads to shorter theorems and proofs and permits the construction of fully adaptive algorithms. Lots of numerical illustrations, comparison tables, and exercises make the text useful in computational mathematics classes. At the same time, the book opens many directions for possible future research.
Reviews / Votes
From the reviews:
"This monograph covers a multitude of Newton methods and presents the algorithms and their convergence analysis from the perspective of affine invariance, which has been the subject of research by the author since 1970. . The book is intended for graduate students of mathematics and computational science and also for researchers in the area of numerical analysis and scientific computing. . As a research monograph, the book not only assembles the current state of the art, but also points to future research prospects." (Gudula Runger, ACM Computing Reviews, June, 2012)
More details
Series
Edition
1st ed. 2004. Corr. 2nd printing 2011
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Primary & secondary/elementary & high school
Illustrations
XII, 424 p. 49 illus.
File size
3,81 MB
ISBN-13
978-3-642-23899-4 (9783642238994)
DOI
10.1007/978-3-642-23899-4
Schweitzer Classification
Other editions
Additional editions
Book
09/2011
Springer
€80.24
Shipment within 7-9 days
Person
Peter Deuflhard is founder and head of the internationally renowned Zuse Institute Berlin (ZIB) and full professor of Numerical Analysis and Scientific Computing at the Free University of Berlin. He is a regular invited speaker at international conferences and universities as well as industry places all over the world.
Content
- Intro
- Newton Methods for Nonlinear Problems
- Preface
- Table of Contents
- Outline of Contents
- 1 Introduction
- Part I ALGEBRAIC EQUATIONS
- 2 Systems of Equations: Local Newton Methods
- 3 Systems of Equations: Global Newton Methods
- 4 Least Squares Problems: Gauss-Newton Methods
- 5 Parameter Dependent Systems: Continuation Methods
- Part II DIFFERENTIAL EQUATIONS
- 6 Stiff ODE Initial Value Problems
- 7 ODE Boundary Value Problems
- 8 PDE Boundary Value Problems
- References
- Software
- Index
