Book reviews
J. Abaffy and E. Spedicato, ABS Projection Algorithms. O-7458-0423-3, 220 pages, a9.95.
319
Ellis Horwood, Chichester, 1989. ISBN
ABS algorithms (named after Abaffy, Broyden and Spedicato) form a large class of projection methods for solving systems of linear and nonlinear equations. This class contains most of the algorithms which are actually known thanks to the possibility of choosing some free parameters. This book presents the first unified treatment of the subject which presently enjoys a regain of interest. The theory given here is quite complete and the book can serve as a basis for the development of new research in this area. It is an important contribution to the literature of numerical analysis. (CB)
S. Vajda, Fibonacci and Lucas Numbers, and the Golden Section. Ellis Horwood, Chichester, 1989. ISBN o-7458-0715-1, 190 pages, &25. Fibonacci numbers and the golden section have attracted the attention of professional and amateur mathematicians for centuries. This is due to their simplicity, their aesthetic properties and their numerous relationships. They also have many applications ranging from Monte-Carlo methods to operation research and search procedures. This book will be the reference on the subject and also on the related Lucas numbers. (CB)
J.R. Partington, An Introduction to Hankel Operators. 1989. ISBN O-521-36791-3, 103 pages, g7.50.
Cambridge University
Press, Cambridge,
This is a particularly well written, clear and easy to follow introduction to Hankel operators. The necessary results from functional analysis and measure theory are gathered in an appendix. The text is short but contains examples and explanations on the theorems and their meaning and implications. It ends with a section containing exercices. A very valuable reference on the subject. (CB)
K.E. Atkinson, Introduction to 50023-2, XVI + 693 pages, 16.50.
Wiley, New York, 1989. ISBN 0-471-
This is the second edition of a book first published in 1978. All the sections were rewritten and new references have been added. New topics are also covered such as trigonometric interpolation, the FFT, numerical differentiation, the method of lines, boundary value problems, the conjugate gradient method and the least squares solutions of systems of linear equations. There is also an appendix on mathematical software. The book can serve as a support for many courses in numerical analysis. (CB)