Newton methods for nonlinear problems: affine invariance and adaptive algorithms
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 affin…
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- Full title :Newton methods for nonlinear problems : affine invariance and adaptive algorithms / Peter Deuflhard.
Summary
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.
Read More ↓Edition Statements
- Publication Date:2011.
Publication Statements
- Publisher(s):Springer
- Place of Publication:Berlin
- Language:eng
- Publication Date:2011.
The Physical Object
- Description:1 online resource (xii, 424 pages)
Edition Identifiers
- ISBN:9783642238994, 3642238998, 9783642238987, 364223898X
- DOI:10.1007/978-3-642-23899-4
- oclc:ocn757379674
- LC Classification:QA297
- Dewey Decimal:518
Table of Contents
pt. 1. Algebraic equations -- pt. 2. Differential equations.
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