It has been 30 years since the publication of Wilkinson's books Rounding Er-
Errors in Algebraic Processes [1088, 1963] and The Algebraic Eigenvalue Prob-
Problem [1089, 1965]. These books provided the first thorough analysis of the
effects of rounding errors on numerical algorithms, and they rapidly became
highly influential classics in numerical analysis. Although a number of more
recent books have included analysis of rounding errors, none has treated the
subject in the same depth as Wilkinson.
This book gives a thorough, up-to-date treatment of the behaviour of
numerical algorithms in finite precision arithmetic. It combines algorithmic
derivations, perturbation theory, and rounding error analysis. Software prac-
practicalities are emphasized throughout, with particular reference to LAPACK.
The best available error bounds, some of them new, are presented in a unified
format with a minimum of jargon. Historical perspective is given to pro-
provide insight into the development of the subject, and further information is
provided in the many quotations. Perturbation theory is treated in detail,
because of its central role in revealing problem sensitivity and providing error
bounds. The book is unique in that algorithmic derivations and motivation
are given succinctly, and implementation details minimized, so that atten-
attention can be concentrated on accuracy and stability results. The book was
designed to be a comprehensive reference and contains extensive citations to
the research literature.
Although the book's main audience is specialists in numerical analysis, it
will be of use to all computational scientists and engineers who are concerned
about the accuracy of their results. Much of the book can be understood with
only a basic grounding in numerical analysis and linear algebra.
This first two chapters are very general. Chapter 1 describes fundamental
concepts of finite precision arithmetic, giving many examples for illustration
and dispelling some misconceptions. Chapter 2 gives a thorough treatment of
floating point arithmetic and may well be the single most useful chapter in the
book. In addition to describing models of floating point arithmetic and the
IEEE standard, it explains how to exploit "low-level" features not represented
in the models and contains a large set of informative exercises.
In the of the book the focus is, inevitably, numerical linear algebra,