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Newton Methods for Nonlinear Problems : Affine Invariance and Adaptive Algorithms / by Peter Deuflhard
Resource type: Ressourcentyp: Buch (Online)Buch (Online)Sprache: Englisch Reihen: Springer Series in Computational Mathematics ; 35 | SpringerLink BücherVerlag: Berlin, Heidelberg : Springer-Verlag Berlin Heidelberg, 2011Beschreibung: Online-Ressource (XII, 424p. 49 illus, digital)ISBN:- 9783642238994
- Nichtlineare algebraische Gleichung
- Nichtlineare Differentialgleichung
- Newton-Verfahren
- Mathematics
- Computer science
- Applied mathematics
- Computer mathematics
- Differential Equations
- Mathematical optimization
- Engineering mathematics
- Gauss-newton methods
- Graduate
- Newton methods
- affine invariance
- continuation methods
- differential equations
- 518
- QA71-90
- QA297
Inhalte:
Zusammenfassung: 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.PPN: PPN: 1651040052Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-SMA
pt. 1. Algebraic equations -- pt. 2. Differential equations.
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