Newton Methods for Nonlinear Problems

Affine Invariance and Adaptive Algorithms

By:

Peter Deuflhard

Format:

Paperback / softback

Series:

Springer Series in Computational Mathematics

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Description

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.

Author Biography:

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.

Release date Australia

September 16th, 2011

Author

Peter Deuflhard

Audience

Professional & Vocational

Illustrations

49 Illustrations, black and white; XII, 424 p. 49 illus.

Pages

424

Series

Springer Series in Computational Mathematics

Dimensions

156x234x22

ISBN-13

9783642238987

Product ID

18347226

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