# Points fixes, zéros et la méthode de Newton / Jean-Pierre Dedieu

Type de document : MonographieCollection : Mathématiques et applications, 54Langue : français.Pays: Allemagne.Éditeur : Berlin : Springer-Verlag, 2006Description : 1 vol. (XII-196 p.) : ill. ; 25 cmISBN: 9783540309956.ISSN: 1154-483X.Bibliographie : Bibliogr. p. [191]-193. Index.Sujet MSC : 65J15, Numerical analysis in abstract spaces, Numerical solutions to equations with nonlinear operators37C25, Smooth dynamical systems: general theory, Fixed points and periodic points of dynamical systems; fixed-point index theory, local dynamics

49M25, Numerical methods in optimal control, Discrete approximations in optimal control

58C15, Global analysis, analysis on manifolds, Implicit function theorems; global Newton methods on manifolds

65H10, Numerical analysis - Nonlinear algebraic or transcendental equations, Numerical computation of solutions to systems of equationsEn-ligne : Springerlink | Zentralblatt

Item type | Current library | Call number | Status | Date due | Barcode |
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Monographie | CMI Salle 1 | Séries SMA (Browse shelf(Opens below)) | Available | 03843-01 |

Bibliogr. p. [191]-193. Index

In the introductory Chapter 1 of the book under review, the author states that the book has its origin in a university course about methods of solving systems of nonlinear equations; but, while making up the redaction of that course more topics have been added, and so the final result is a book containing much more than the things that he had originally in mind. Hence, the author has produced a book of 196 pages, structured as follows: Chapter 1: Introduction (pp. 1–3); Chapter 2: Fixed points (pp. 5–74); Chapter 3: Newton’s method (pp. 75–110); Chapter 4: Newton’s method for underdetermined systems (pp. 111–144); Chapter 5: The method of Newton-Gauss for overdetermined systems (pp. 145–175); Chapter 6: Appendices (pp. 177–190). The book ends with a list of 57 references (pp. 191–193) and an index (pp. 195–196).

Returning to the introductory Chapter 1, the author states that the book is intended for students doing higher level studies in mathematics, and for researchers. What is needed for reading it, he says, is a good knowledge of linear algebra, general topology and differential calculus, and some knowledge of functional analysis and of complex variables. The potential reader should also know that the two general frames in which the results are stated are either Banach spaces or Hilbert spaces (a few results are stated in complete metric spaces). In order to make the book in some sense “self-contained", the author has added the appendices in Chapter 6, containing a.o. some definitions and results about differential calculus on Banach spaces, on Hilbert spaces and on Euclidean spaces. ... (Zentralblatt)

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