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Original Essays | November 5, 2009

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Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms

by Peter (konrad-zuse-zentrum Berlin, Berlin-dahlem, Germany) Deuflhard

Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms Cover

Synopses & Reviews

Publisher Comments:

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.
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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.
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Product Details

ISBN:
9783540210993
Subtitle:
Affine Invariance and Adaptive Algorithms
Author:
Deuflhard, Peter (konrad-zuse-zentrum Berlin, Berlin-dahlem, Germany)
Author:
Deuflhard, Peter
Publisher:
Springer Berlin Heidelberg
Subject:
Differential Equations
Subject:
Number Systems
Subject:
Continuation methods.
Subject:
Newton methods
Subject:
affine invariance
Subject:
Gauss-newton methods
Subject:
Computer Science
Copyright:
2004
Edition Number:
1
Edition Description:
2004. Corr. 2nd
Series:
Springer Series in Computational Mathematics
Series Volume:
35
Publication Date:
January 2005
Binding:
Hardcover
Language:
English
Illustrations:
Y
Pages:
424
Dimensions:
9.21x6.14x1.00 in. 1.74 lbs.
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