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Book 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. 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.

Book details

Book category Books in English Mathematics & science Mathematics Calculus & mathematical analysis

• Full title: Newton Methods for Nonlinear Problems
• Subtitle: Affine Invariance and Adaptive Algorithms
• Author: Peter Deuflhard
• Language: English
• Binding: Paperback
• Number of pages: 424
• EAN: 9783642059278
• ISBN: 3642059279
• ID: 05281006
• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
• Weight: 670 g
• Dimensions: 25 × 168 × 24 mm
• Date of publishing: 01. December 2010

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