Boston: Birkhäuser. xiii, 506 p. DM 118.00; öS 862.00; sFr 98.00 (1997).
No doubt, this is an excellent book of 506 pages on Numerical analysis written by an experienced teacher and researcher in this area. So, what are the differences to other existing excellent and classical books on this subject? As the author states, the first four chapters (Machine arithmetic and related matters, Approximation and interpolation, Numerical differentiation and integration, Nonlinear equations) could serve as a text for a basic introductory course and the three remaining chapters (One- and multistep methods and Two-point boundary value problems for ordinary differential equations) could provide a text for some advanced course. Therefore the appendix “An introduction” is misleading.
Nevertheless, the concept will be OK for a graduate program in Numerical analysis in the U.S.A. which is completed by courses at least on Numerical linear algebra. In Germany, if not in Europe, it ought to be more common to include in such a textbook Gaussian elimination and basic iterative methods for linear systems of equations, overdetermined linear systems, and adaptive numerical integration and hence to reduce the size of the last three chapters.