for systems of linear equations, to name a few. They have many applications, in particular, in physics and chemistry.
The aim of this book is to give an overview of these questions and to show that a profound understanding of asymptotic expansions is necessary to comprehend extrapolation methods seriously. The author has himself contributed significantly to both subjects.
The first part of the book deals with asymptotic expansions: asymptotic systems and expansions, geometric asymptotic expansions, and logarithmic asymptotic expansions. The second part of the book is devoted to linear extrapolation methods: fundamental concepts and general philosophy, error bounds, stopping rules and monotonicity, generalizations, and final remarks. Historical notes and numerical examples have also been included.
This book is well written, well presented, easy to read, and, which is not so common, well printed. It is an important addition to the literature (which is not so abundant) on these topics. It could be used for a course on these questions and it is highly recommended to researchers and to all those who need to use convergence acceleration methods.
Claude Brezinski E-mail: Claude.BrezinskiΓuniv-lille1.fr article no. AT973145