Analyse numérique / J. Baranger ; avec la collaboration de Claude Brezinski, Claude Carasso, Jean-Marc Chassery... [et al.]

This book – intended for second year students (in a French system of university education) – gives a survey of classical and more recent methods of numerical mathematics together with an insight into its philosophy. The first part, due to J. Baranger, deals with the fundamental methods: basic methods of numerical algebra in an n-dimensional space (solution of linear and nonlinear systems), methods for the numerical solution of functional equations (this means problems for differential equations, also in variational formulation, up to parabolic equations of evolution), and methods to approximate functions (interpolation and norm approximation, including numerical integration). The second part, due to seven specialists, repeats these subjects and gives a deeper insight into remedies for special, more complicated situations: large linear and nonlinear systems ( gradient methods with preconditioning, too, resp. quasi-Newton methods), more issues of eigenvalues and eigenvectors (due to F. Chatelin), in the reviewer's opinion a presentation with a highly interesting frame), approximation by splines and Padé approximations, fast Fourier transforms, and stiff differential equations. Everywhere exercises and problems for programming are added. References (not everywhere up to date) and useful comments on them are found. Hence, this is a textbook sufficient to give an appropriate, authentic knowledge of numerical mathematics, especially (caused by the reasonably low amount of functional analysis) for those who are interested in applications (as students of science or engineering, too). (Zentralblatt)

Bibliogr. à la fin de chaque partie. Index