Mathématiques et Applications

Points fixes, zéros et la méthode de Newton

Authors: Dedieu, Jean-Pierre

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About this Textbook

Cet ouvrage est consacré aux points fixes d'applications différentiables, aux zéros de systèmes non-linéaires et à la méthode de Newton. Il s'adresse à des étudiants de mastère ou préparant l'agrégation de mathématique et à des chercheurs confirmés. La première partie est consacrée à la méthode des approximations successives et confronte un point de vue «systèmes dynamiques» (théorèmes de Grobman-Hartman, de la variété stable) à des exemples issus de l'analyse numérique. La seconde partie de cet ouvrage expose la méthode de Newton et ses développements les plus récents (théorie alpha de Smale, systèmes sous ou sur-déterminés). Elle présente une nouvelle approche de ce sujet et un ensemble de résultats originaux publiés pour la première fois dans un ouvrage de langue française.

This is an advanced text on fixed points, zeros of nonlinear systems and the Newton method. Its first part, devoted to fixed points, includes the Grobman-Hartman and the stable manifold theorems. The second part describes the Newton method from a modern point of view: Smale's alpha theory, underdetermined and overdetermined systems of equations. These results are illustrated by various examples from numerical analysis.

Reviews

From the reviews:

“Fixed point schemes are an important tool in pure and applied mathematics. This book offers a good introduction to them and in particular provides an in depth treatment of the Newton method. … A very nice feature of this book is the many interesting examples that accompany each chapter. … The book is carefully crafted and well written. As it is mostly self contained and possesses several appendices recalling the basic notions, it should be accessible to master students.” (Christophe Troestler, Bulletin of the Belgian Mathematical Society, Vol. 15 (1), 2008)

Table of contents (2 chapters)

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-3-540-37660-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $79.95
price for USA
  • ISBN 978-3-540-30995-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Points fixes, zéros et la méthode de Newton
Authors
Series Title
Mathématiques et Applications
Series Volume
54
Copyright
2006
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-37660-6
DOI
10.1007/3-540-37660-7
Softcover ISBN
978-3-540-30995-6
Series ISSN
1154-483X
Edition Number
1
Number of Pages
XII, 196
Number of Illustrations and Tables
7 b/w illustrations
Topics