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

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)