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Numerical recipes. The art of scientific computing. (English) Zbl 0587.65003
Cambridge etc.: Cambridge University Press. XX, 818 p. £ 25.00; $ 39.50 (1986).
This book represents a generous benefit of the numerical and computational experience of four leading scientists in academic research and industry. Both for inexperienced and advanced users of computer methods, for physicists and engineers faced with practical problems, ”Numerical recipes” will constitute a reference text on the art of scientific computation, offering, for each topic considered, a certain amount of general discussion, adequate mathematical prerequisites, comparisons of the nature of the computational algorithms and practical questions of implementation in working routines.
The scope of ”Numerical recipes” (affirmed by the authors themselves) is to be ”everything up to, but not including, partial differential equations”, although the last chapter realizes a consistent introduction to numerical methods for PDE. Besides the so-called ”standard” topics of a numerical analysis course (solution of linear algebraic equations, interpolation and extrapolation, integration of functions, root findings and nonlinear sets of equations, minimization or maximization of functions, eigensystems, integration of ordinary differential equations), this approach also covers less usual, but highly useful subjects, as: evaluation of particular special functions in higher mathematics, random numbers and Monte Carlo methods, sorting, Fourier transform and spectral methods, statistical description and modeling of data, two point boundary value problems.
There are approximately 200 subroutines or functions, amply commented in the book, each one both in FORTRAN and in Pascal; two example books published by the same authors to accompany ”Numerical recipes” (reviewed below), contain their FORTRAN and respectively Pascal test-drivers. All the procedures listed in ”Numerical recipes” are available from Cambridge University Press on diskettes for IBM compatible machines.
The main idea governing the spirit of the book is to ”open up a large number of computational black boxes to reader’s scrutiny” and points out the same fundamental principle expressed by G. E. Forsythe, M. A. Malcolm and C. B. Moler in their well known ”Computer methods for mathematical computations” (1977; Zbl 0361.65002): ”There is a wealth of pitfalls in numerical computation. The student should learn to look for the symptoms of numerical ill health and to correctly diagnose the problems.”
Reviewer: O.Pastravanu

MSC:
65-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis
65Fxx Numerical linear algebra
65Dxx Numerical approximation and computational geometry (primarily algorithms)
65C10 Random number generation in numerical analysis
68P10 Searching and sorting
65Hxx Nonlinear algebraic or transcendental equations
65K05 Numerical mathematical programming methods
65T40 Numerical methods for trigonometric approximation and interpolation
65C99 Probabilistic methods, stochastic differential equations
65Lxx Numerical methods for ordinary differential equations
65Mxx Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65Nxx Numerical methods for partial differential equations, boundary value problems
15-04 Software, source code, etc. for problems pertaining to linear algebra
41-04 Software, source code, etc. for problems pertaining to approximations and expansions
33-04 Software, source code, etc. for problems pertaining to special functions
68-04 Software, source code, etc. for problems pertaining to computer science
90-04 Software, source code, etc. for problems pertaining to operations research and mathematical programming
42-04 Software, source code, etc. for problems pertaining to harmonic analysis on Euclidean spaces
62-04 Software, source code, etc. for problems pertaining to statistics
34-04 Software, source code, etc. for problems pertaining to ordinary differential equations
35-04 Software, source code, etc. for problems pertaining to partial differential equations