Newton Methods for Nonlinear Problems
Affine Invariance and Adaptive Algorithms
Authors: Deuflhard, Peter
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- About this Textbook
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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.
- About the authors
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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.
- Reviews
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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)
- Table of contents (8 chapters)
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Introduction
Pages 7-41
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Systems of Equations: Local Newton Methods
Pages 45-107
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Systems of Equations: Global Newton Methods
Pages 109-172
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Least Squares Problems: Gauss-Newton Methods
Pages 173-231
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Parameter Dependent Systems: Continuation Methods
Pages 233-282
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Table of contents (8 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Newton Methods for Nonlinear Problems
- Book Subtitle
- Affine Invariance and Adaptive Algorithms
- Authors
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- Peter Deuflhard
- Series Title
- Springer Series in Computational Mathematics
- Series Volume
- 35
- Copyright
- 2011
- Publisher
- Springer-Verlag Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- eBook ISBN
- 978-3-642-23899-4
- DOI
- 10.1007/978-3-642-23899-4
- Softcover ISBN
- 978-3-642-23898-7
- Series ISSN
- 0179-3632
- Edition Number
- 1
- Number of Pages
- XII, 424
- Number of Illustrations
- 49 b/w illustrations
- Topics
