
Author(s)  Chatelin, Francoise 

Title  Eigenvalues of Matrices 
Publisher  John Wiley & Sons 
Year of publication  1993 
Reviewed by  VioricaCerasela Postolache 
Various problems of modelling of technical phenomena lead to the necessity of solving eigenproblems. An example is provided by the dynamic analysis of structures modelled by the finite elements technique. This book provides fundamental notions and results concerning eigenvalues solution techniques and their applications in probability theory, the dynamic of structures, chemistry, etc. The work gives a sufficient number of results, so as to permit the reader to give an orientation in some important topics of Applied Mathematics.
The book includes seven chapters, a preface, a comprehensive bibliography, a table of index, a table of contents sufficiently detailed as well as a section containing the main notations used in the book. Also an appendix containing solution of some exercises is included. The first of these chapters deals with some supplements from linear algebra. The second gives the basic elements of the spectral theory. In the third chapter a motivation why is necessary to compute eigenvalues is presented. Chapter 4 deals with the error analysis and in Chapter 5 are investigated the foundations of methods for computing eigenvalues. In Chapter 6 numerical methods for large matrices such that subspace iteration method, Lanczos method, etc. are presented. In the last chapter Chebyshev's iterative methods are treated. Each chapter is finished by interesting bibliographical comments.
Due to its elementary level, this book is suitable for more advanced students in mathematics, engineering, physics and chemistry, as well as for applied mathematicians engineers and computer scientists interested in the topic of the eigenvalues finding. An introductory course to calculus is assumed.
The presentation of the book is rigorous, strict proofs of the stated results are given. The book is sufficiently self contained to enable independent research. Many examples and carefully plotted pictures illustrate the ideas and the concepts. Also, the book contains a lot of applied problems (written together Prof. Ahués) collected from a book already published by the two authors. Purchasing this book is a good investment for individuals and libraries alike.