Boca Raton, FL: CRC Press. xvii, 795 p. with disc (1995).
The computational methods in regular use at the Mathematical Centre, Amsterdam, have been described and assembled in the form of a numerical algorithms library written in Algol 60 [cf. P. W. Hemker (Ed.), NUMAL, Numerical procedures in Algol 60, MC Syllabus 47.1-47.7, Mathematical Centre, Amsterdam (1981; Zbl 0457.65001)]. The methods relate to linear algebra, optimization, parameter estimation, special functions of mathematical physics and the numerical solution of ordinary and partial differential equations. The latter section, concerning a subject to which members of the centre have made notable contributions, is particularly impressive. Comparative reviews of the library and the software collections IMSL (Houston, Texas) and NAG (Oxford), both entitled “Colloquium Numerieke Programmatuur”, are contained in J. C. P. Bus (Ed.), MC Syllabus NR 29.1a, b (1976) and H. J. J. te Riele (Ed.), MC Syllabus NR 29.2 (1977), both published by the Mathematical Centre, Amsterdam. A FORTRAN version of the library has been constructed by the reviewer: NUMAL in FORTRAN, IIMAS Universidad Nacional Autónoma de México, Comunicaciones técnicas Nos. 48.0-48.11 (1981).
The highly modular construction of the library renders it particulary suitable for use on personal computers, most of which are provided with a -language compiler. The volume under review offers a version of NUMAL. There are a few minor blemishes (e.g. in some places lines of procedure description are out of order) but these can easily be removed in subsequent expansions and re-editions of the library. The theoretical descriptions given by W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery [Numerical recipes in . The art of scientific computing. 2nd ed. (1992)] are more extensive, but the library under review, which is intended primarily as a research tool, is more complete and the technology which it contains is far more powerful. The version of NUMAL is of considerable potential significance to working mathematicians many of whom can afford to buy, and indeed already own, a personal computer. With this library they acquire the computational capability of a leading research centre.