
Author(s) 
Godunov, S.K. Antonov, A.G. Kiriljuk, O.P. Kostin, V.I. 

Title  Guaranteed Accuracy in Numerical Linear Algebra 
Publisher  Kluwer Academic Publishers 
Year of publication  1993 
Reviewed by  Mihai Postolache 
Numerical linear algebra as branch of numerical analysis is relevant in various fields of science and technology. This is a very specialized monograph which presents a coherent exposition of some important techniques, methods and results concerning linear systems solving whose coefficient matrices has given special forms. Also, some important machine realizations of the treated algorithms are given (for instance, error analysis, solving systems with bidiagonal coefficients matrices, computer realization of the deflation algorithm and so on).
The book includes five chapters, an introduction, bibliography, table of index, table of contents sufficiently detailed. The first of these chapters deals with singular value decomposition. This chapter includes a discussion about elementary orthogonal transformations, numerical characteristics of matrices, the deflation process etc. The second, gives the basic elements concerning the systems of linear equations such that: the condition number, generalized normal solutions and resolutions. In the third chapter, deflation algorithms for band matrices are presented. Chapter 4, deals with the Sturm sequences of tridiagonal matrices and in Chapter 5 are investigated the peculiarities of computer computations. Here it can found some computer models and numerical examples which illustrate the main concepts. This book is very well produced.
Written for more advanced students in mathematics, graduate students, research scientists as well as for applied mathematicians, this book provides a detailed investigation of some important techniques for numerical solving of linear systems. This topic is fundamental in structural analysis, mechanics, the theory of operator equations and so on. Parts of this book will be useful for biologists, applied physicists etc. An introductory course to linear algebra, is assumed.
Generally speaking, the presentation of the book is very rigorous, strict proofs of the stated results are given. But the notation is adequate and the concepts are clearly presented. The book is sufficiently self contained to enable independent research. Purchasing this book is a good investment for individuals as well as for libraries alike.