Springer Series in Computational Mathematics

Newton Methods for Nonlinear Problems

Affine Invariance and Adaptive Algorithms

Authors: Deuflhard, Peter

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About this Textbook

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

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

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)

  • Introduction

    Deuflhard, Peter

    Pages 7-41

  • Systems of Equations: Local Newton Methods

    Deuflhard, Peter

    Pages 45-107

  • Systems of Equations: Global Newton Methods

    Deuflhard, Peter

    Pages 109-172

  • Least Squares Problems: Gauss-Newton Methods

    Deuflhard, Peter

    Pages 173-231

  • Parameter Dependent Systems: Continuation Methods

    Deuflhard, Peter

    Pages 233-282

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-642-23899-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $74.95
price for USA
  • ISBN 978-3-642-23898-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Newton Methods for Nonlinear Problems
Book Subtitle
Affine Invariance and Adaptive Algorithms
Authors
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 and Tables
49 b/w illustrations
Topics