BOOK REVIEWS 691

certain that further connections will be discov-ered between extremal combinatorics and com-putational geometry. For researchers it is essen-tial to understand and be able to use these up-to-date techniques. This book is written by twoleading researchers in computational geometry.This fact guarantees that the book fulfills the ex-pectation of the reader.

The first four chapters, extended with selectedtopics from the further parts of the book, is suit-able for an advanced class for graduate studentsin computer science or in combinatorics.

The book is very important to any specialist incomputational geometry, combinatorial geome-try, or combinatorics. It is highly recommendedto anybody who is interested in this new topic atthe border of combinatorics, geometry, and algo-rithm theory.

PETER HAJNALBolyai Institute

Lyapunov Matrix Equation in System Stabil-ity and Control. By Zoran Gajic. and Muham-mad Tahir Javed Qureshi. Academic Press, SanDiego, CA, 1995. xii + 255 pp., cloth. ISBN0-12-273370-3. Mathematics in Science and En-gineering, Vol. 195.

to singularly perturbed and weakly coupled sys-tems are presented. Chapter 6 studies qualitativeproperties such as the stability robustness of lin-ear systems and the sensitivity of the algebraicLyapunov equation. Parallel algorithms and iter-ative methods for solving large scale Lyapunovequations are presented in Chapter 7 while Lya-punov iterations for solving nonlinear algebraicequations arising in control theory are treated inChapter 8. The last chapter contains a brief re-view of Lyapunov-like equations and commentson related topics. Then, in an Appendix, somematrix inequalities appearing in the book are sum-marized.

This textbook is intended for a wide readershipincluding engineers, applied mathematicians,computer scientists, and graduate students whoseek a comprehensive view of the main results ofthe Lyapunov matrix equation updated to 1994.

Apart from short proofs of some of the pre-sented results, for proofs of many important factsthe reader is referred to original papers. Thus, thebook is far from being a self-contained one, butwould be very appreciated in graduate coursestargeted for engineers and applied mathemati-cians. The price is reasonable.

LUCAS JODARUniversidad Politdcnica de Valencia

This book provides important and useful infor-mation related to the solutions of the Lyapunovmatrix equation for both the algebraic and thedifferential cases and for both continuous-timeand discrete-time systems. Some real world sys-tems, whose analysis and design are related tothe Lyapunov equations, are presented through-out the book, making the reading pleasant.

Chapter contains a motivating introductionwhich emphasizes the importance of the Lya-punov equation in engineering and science byindicating many areas of applications. In termsof the relevance and amount of information pro-vided, a main part of the book lies in Chapters 2,3, and 4. In these, methods for explicit solutions,numerical solutions, and bounds of solutions’ at-tributes, such as eigenvalues, trace, and determi-nant bounds, are presented. Chapter 2 discussesthe continuous-time algebraic Lyapunov equa-tion corresponding to continuous-time systems.The discrete-time algebraic equation is studiedin Chapter 3, and Chapter 4 deals with the differ-ential and difference Lyapunov equations.

In Chapter 5, solutions of algebraic Lyapunovequations with small parameters corresponding

CRC Standard Mathematical Tables and For-mulae. Edited by Daniel Zwillinger. CRC Press,Inc., Boca Raton, FL, 1996. $39.95. 812 pp.,cloth. ISBN 0-8493-2479-3.

Those of a certain generation will remember theChemical Rubber Company Tables of their stu-dent days, extracted from a larger Handbook ofChemistry and Physics, which contains log andtrig tables as well as the ever-useful tables of inte-grals and mathematical miscellanea such as thosepesky hyperbolic identities.

This latest incarnation is larger than the oldHandbook and is full ofmathematical facts, mak-ing it a very useful volume. The information con-sists of a bare statement of definitions, facts, for-mulas, and tables of information, diagrams, andillustrations. The following discussion does notdo justice to the wealth of information containedin this book.

There are 10 chapters. The first chapter, "Anal-ysis" (74 pp.), contains the usual infinite sums andproducts and a variety of other information such

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