Authors:
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Series in Computational Mathematics (SSCM, volume 35)
Buy it now
Buying options
Tax calculation will be finalised at checkout
Other ways to access
About this book
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.
Keywords
- Gauss-newton methods
- Newton methods
- affine invariance
- continuation methods
- differential equations
- ordinary differential equations
Authors and Affiliations
-
Abt. Numerische Analysis und Modellierung, Zuse-Institut Berlin (ZIB), Berlin, Germany
Peter Deuflhard
About the author
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.
Bibliographic Information
Book Title: Newton Methods for Nonlinear Problems
Book Subtitle: Affine Invariance and Adaptive Algorithms
Authors: Peter Deuflhard
Series Title: Springer Series in Computational Mathematics
Publisher: Springer Berlin, Heidelberg
Copyright Information: Springer-Verlag Berlin Heidelberg 2004
Hardcover ISBN: 978-3-540-21099-3Published: 26 April 2004
Softcover ISBN: 978-3-642-05927-8Published: 01 December 2010
Series ISSN: 0179-3632
Series E-ISSN: 2198-3712
Edition Number: 1
Number of Pages: XII, 424
Number of Illustrations: 48 b/w illustrations