Résolution numérique des grands systèmes linéaires. (École d’été d’analyse numérique, CEA-EDF-INRIA, 1980). Préface de Robert Dautray. (French) Zbl 0646.65022

Golub, Gene H.; Meurant, Gérard A.

Collection de la Direction des Études et Recherches d’Électricité de France, 49. Paris: Éditions Eyrolles. VIII, 329 p. (1983).

These lecture notes, originating from a Summer School given in 1980 are distinguished by the original choice of topics, revealing the identity of the first author, and care of detail and proper (French) language, characteristic of the second author. First least squares problems are treated, beginning with norms, elementary transformations, ending with large dissected geodetic networks. Second fast Poisson solvers based on FFT and odd even reduction are treated. Third iterative methods are started with the standard SOR theory, continued with the unjustly forgotten Richardson scheme and concluded with the current preconditioned c-g methods. In the final chapter all methods discussed are compared on a test example. This results in a series of diagrams where the reader can see black on white how all the theories fall out in practice.

Reviewer: A.Ruhe

MSC:

65Fxx	Numerical linear algebra
65-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis
65N22	Numerical solution of discretized equations for boundary value problems involving PDEs

Keywords:

numerical examples; fast Fourier transform; successive overrelaxation; preconditioned conjugate gradient methods; least squares problems; geodetic networks; fast Poisson solvers; odd even reduction; Richardson scheme