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Book review

Author(s) Lascaux, P.
Théodor, R.
Title Analyse numérique matricielle appliquée à l'art de l'ingénieur
Publisher Masson
Year of publication 1993
Reviewed by Viorica-Cerasela Postolache

Many important phenomena are described by means of mathematical models which involve numerical analysis. To understand these phenomena necessarily implies being able to solve linear and non-linear equations, to find eigenvectors and eigenvalues and so on. The book provides a systematic and modern presentation of the most important direct methods and techniques of numerical analysis using interrelations with digital computers.

The text has been written for a wide range of readers whose work involves the numerical analysis such that: engineers, applied mathematicians, undergraduate and postgraduate students.

The authors discuss the sources of this branch in mathematical analysis, develop main concepts and results, and mention some beautiful theorems. The relationship to finite element method, to finite difference method is considered. In this book can be found examples from structural mechanics and physics. The treatment assumes a familiarity with only a few fundamental concepts from calculus, matrix algebra and computers. However this book is sufficiently self contained to enable independent research. Consequently a large area of readers can use the book.

Contents: A comprehensive introduction, Examples of modelling problems, Conditioning, Direct methods for linear systems solving, Direct methods for matrices with large dimensions, Least squares methods. The book is very interesting because contains some concepts such that: incomplete factorization, bandwidth minimization, Cuthill Mac Kee algorithms for nodal numbering optimization which are very rare presented in books of numerical analysis. Also, a large number of exercises lead to individual experimental work and independent study.

There exists a table of index and the table of contents is sufficiently detailed. Numerous pictures, carefully plotted, illustrate the ideas and the concepts. The book is very well produced. Generally, the presentation is rigorous and reflects the experience of the two authors in numerical analysis research work. Since numerical analysis is relevant in various life and social sciences, I expect that this book will be of interest to workers in these fields and all those who can read French. I strongly recommend it to all scientists seriously wishing to learn about numerical methods and their main applications in engineering. Is not necessary to pay attention to the few graphical omissions of this edition (on p. 151 || B A - I, on p. 292 Définbition).