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Newton Methods for Nonlinear Problems : Affine Invariance and Adaptive Algorithms - Peter Deuflhard

Newton Methods for Nonlinear Problems

Affine Invariance and Adaptive Algorithms

Hardcover Published: 13th January 2005
ISBN: 9783540210993
Number Of Pages: 424

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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.

Introductionp. 7
Systems of equations : local Newton methodsp. 45
Systems of equations : global Newton methodsp. 109
Least squares problems : Gauss-Newton methodsp. 173
Parameter dependent systems : continuation methodsp. 233
Stiff ODE initial value problemsp. 285
ODE boundary value problemsp. 315
PDE boundary value problemsp. 369
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783540210993
ISBN-10: 3540210997
Series: Springer Series in Computational Mathematics
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 424
Published: 13th January 2005
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 2.54
Weight (kg): 0.79