Alternatives to Numerical Recipes
There is no single alternative to Numerical Recipes. The authors of Numerical
Recipes provide a superficial overview of a large amount of material in a small
volume. In order to do so, they made many unfortunate compromises.
It is naïve to hope that every computational problem can be solved by a
simple procedure that can be described in a few pages of chatty prose,
and using a page or two of Fortran or C code. Today's ambitions for
correctness, accuracy, precision, stability, "robustness", efficiency, etc.
demand sophisticated codes developed by experts with deep understanding of
their disciplines. We have long ago outgrown the capabilities of the
simplistic approaches of 30 years ago.
Steve Sullivan has constructed a
FAQ (Frequently Asked Questions) list on numerical analysis. The size of
the list will give you some idea of the scope of the field. Some books are
reviewed in section q165.
It would be unproductive to try to list all the excellent textbooks on
numerical analysis. A few of them are (in alphabetical order of primary
There are excellent texts and reference works that focus on narrow portions of
the discipline of numerical analysis. Consider, for example:
- Kendall Atkinson, Numerical Analysis.
- Ward Cheney and David Kincaid, Numerical Mathematics and Computing,
Brooks-Cole (Third edition, 1994). Aharon Naiman has prepared slides for a series of
he teaches at Jerusalem College of Technology using this text.
- George Forsythe, Michael Malcolm and Cleve Moler, Computer Methods
for Mathematical Computations, Prentice-Hall (1977). This book is
probably out of print. It is a predecessor to the book by Kahaner et. al.,
and written in a similar style. It is less comprehensive than the newer work.
- Francis B. Hildebrand, Introduction to Numerical Analysis,
McGraw-Hill (1956, 1974), Dover (1987 0-486-65363-3). This is one of the
best books ever written on numerical analysis. It's out-of-date in some
areas, most notably in Least Squares computation. Hildebrand has an engaging
and transparent style of exposition, similar to Press et. al. This book is,
however, a mathematically sound reference to material of the same era as
presented in much of Numerical Recipes.
- David Kahaner, Cleve Moler and John Nash, Numerical Methods and
Software, Prentice-Hall (1989). ISBN 0-13-627258-4. This book is probably
closest in style to Numerical Recipes, but was written by
practitioners in the field, rather then by experts in a different field.
- John H. Mathews,
Methods: for Mathematics, Science & Engineering, 2nd Ed., ISBN
0-13-624990-6 and 0-13-625047-5, Prentice
Hall Inc. (1992).   With purchase of this book free software is
available from the following links:
- John H. Mathews and Russell W. Howell,
COMPLEX ANALYSIS: for
Engineering, Third Edition, 1997, ISBN 0-7637-0270-6.
With purchase of this book, free software is
- Zdzislaw Meglicki has posted
the text for a course on advanced scientific computing at Indiana
- G. W. "Pete" Stewart posted the following in
"I have recently published a book entitled `Afternotes on Numerical
Analysis'... It is a series of 22 lectures on elementary numerical
analysis. The notes themselves were prepared after the lectures were given
and are an accurate snapshot of what went on in class. Although they are
no substitute for a full-blown numerical analysis textbook, many people
have found them a useful supplement to a first course. The book is
published by SIAM. For further information contact email@example.com."
and on 2 Jan 1997:
I have just completed a new set of afternotes and have posted them on
the web. The original afternotes were based on an advanced
undergraduate course taught at the University of Maryland. The
present notes are based on the follow-up graduate course. The topics
treated are approximation\,---\,discrete and continuous\,---\,linear
and quadratic splines, eigensystems, and Krylov sequence methods. The
notes conclude with two little lectures on classical iterative methods
and nonlinear equations
The notes may be obtained by anonymous ftp at thales.cs.umd.edu in
/pub/afternotes or by browsing my homepage
I will be grateful for any comments, corrections, or suggestions.
If you have been using Numerical Recipes for software, we recommend that
you contact the computing professionals in your organization. For JPL
users, you can contact the
Subgroup, or obtain the
mathc90 libraries of mathematical software directly. There is also
a substantial amount of
software and information
about software on-line.
- Gene H. Golub and Charles F. Van Loan, Matrix Computations,
Johns Hopkins (first edition 1983, second edition 1989, third edition
1996). ISBN 0-8018-5413-X (0-8018-5414-8 paper).
- Ernst Hairer, Syvert Paul Nørsett, Gerhard Wanner, Solving Ordinary
Differential Equations I: Nonstiff Problems, Springer-Verlag (1987
3-540-17145-2 0-387-17145-2). A second edition has appeared but the
ISBN's here are for the first.
- Ernst Hairer, Gerhard Wanner, Solving Ordinary Differential Equations
II: Stiff and Differential-Algebraic Problems, Springer-Verlag (1991:
3-540-53775-9 and 0-387-53775-9; 1996: 3-540-60452-9). This book and the
previous one are highly regarded.
- Charles L. Lawson and Richard J. Hanson, Solving Least Squares
Problems, Prentice-Hall (first edition 1974), SIAM Press (second edition
1995) ISBN 0-89871-356-0.
- Philip J. Davis and Philip Rabinowitz, Methods of Numerical
Integration, Academic Press (second edition 1984) ISBN 0-12-206360-0.
- Ingrid Daubechies, Ten Lectures on Wavelets, SIAM Press.
- Jorge J. Moré and Stephen J. Wright, Optimization Software
Guide, Frontiers in Applied Mathematics 14, Society for Industrial
and Applied Mathematics (1993). About evenly divided between algorithms and
software, both public-domain and commercial. (This book actually covers a
fair amount of the content of Numerical Recipes, especially those
parts that the authors of NR deemed too complex to do well.)
- Spaeth, Mathematical Algorithms for Linear Regression (1987).
For one-of-a-kind computations, we recommend
MATLAB (The MathWorks, Inc.).
Revised: November 16, 2001