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Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms

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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.

Synopsis:

This book deals with the efficient numerical solution of challenging nonlinear problems in science and engineering, both in finite and in infinite dimension. Its focus is on local and global Newton methods for direct problems or Gauss-Newton methods for inverse problems. 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 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.

Product Details

ISBN:
9783540210993
Author:
Deuflhard, Peter (konrad-zuse-zentrum Berlin, Berlin-dahlem, Germany)
Publisher:
Springer
Author:
Deuflhard, Peter
Subject:
Differential Equations
Subject:
Number Systems
Subject:
Continuation methods.
Subject:
Newton methods
Subject:
affine invariance
Subject:
Gauss-newton methods
Subject:
Computer Science
Subject:
Computational Mathematics and Numerical Analysis
Subject:
Computational science and engineering
Subject:
ordinary differential equations
Subject:
Appl.Mathematics/Computational Methods of Engineering
Subject:
OPTIMIZATION
Subject:
Math Applications in Computer Science
Subject:
Mathematics-Introduction
Subject:
Counting & Numeration
Copyright:
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:
436
Dimensions:
235 x 155 mm 1750 gr

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Related Subjects

Computers and Internet » Computers Reference » General
Computers and Internet » Personal Computers » General
Reference » Science Reference » Technology
Science and Mathematics » Mathematics » Differential Equations
Science and Mathematics » Mathematics » Foundations and Logic
Science and Mathematics » Mathematics » Introduction
Science and Mathematics » Physics » General

Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms New Hardcover
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$150.50 In Stock
Product details 436 pages Springer - English 9783540210993 Reviews:
"Synopsis" by , This book deals with the efficient numerical solution of challenging nonlinear problems in science and engineering, both in finite and in infinite dimension. Its focus is on local and global Newton methods for direct problems or Gauss-Newton methods for inverse problems. 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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