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Acton, Forman S. 1990, Numerical methods that [usually] work, Harper & Row, Publishers, ISBN 0883854503. [Daniel Pick] This book is almost worth its price just for the cathartic interlude in the middle of the book on what not to compute. You should require your students to read it, learn it, live it. You may find just giving them the railroad problem found at the beginning of the book a worthwhile exercise. [Bill Frensley] Amen, brother! The only complaint that I have about Acton's interlude is that after demolishing the notion of "fitting exponential data," he fails to point out that this is the inverse Laplace transform problem. Perhaps if everyone read this and made the connection, we would be spared the monthly "is there any good algorithm for the inverse Laplace transform?"

Arge, Bruaset and Langtangen, editors, Modern Software Tools for Scientific Computing. Contains selected contributions from the SciTools'96 conference.

Baker, Louis. 1991, C Mathematical Function Handbook

Daehlen and Tveito, editors, Numerical Methods and Software Tools in Industrial Mathematics, Birkhauser It includes an introduction to object-oriented numerics and a presentation of the software tools Diffpack and Siscat.

Dahlquist, Germund; Bjorck, Ake, 1974, Numerical Methods translated by Ned Anderson, Prentice-Hall, 1974. A nice mix of theory and practice. Used as a text at Stanford, among other places.[John Chandler]

Dubois, Paul. 1996, Object Technology for Scientific Computing, Object-Oriented Numerical Software in Eiffel and C, Prentice Hall, 1996, paper, 350 pages ISBN 0-13-267808-X

Duff, I.S., and G.A. Watson, editors, 1996, The State of the Art in Numerical Analysis. The 1996 conference on the State of the Art in Numerical Analysis was organized to provide the numerical analysis community, and users of numerical methods, with a forum where an account of the important recent developments in the subject could be presented in a coherent and concentrated way in a manner accessible to the non-specialist in the sub-area.

Forsythe, George; Moler, Cleve B. 1967, "Computer Solution of Linear Algebraic Systems", Prentice-Hall I consider this possibly the best textbook I have ever seen in any field. Covers only linear systems, of course.[John Chandler]

Gautschi, Walter, 1997, Numerical analysis : an introduction, Boston, Mass. : Birkhauser, 1997 A very readable, carefully written book with emphasis on nonlinear aspects of numerical analysis. The book is suitable for a first year graduate course and contains a rich set of examples and exercises. [Jorg Peters]

Golub, Gene H.; Van Loan, Charles F., 1996, Matrix Computations, Third edition, Johns Hopkins, Baltimore, ISBN 0-8018-3739-1, [SJS] A classic for handling matrices. Many current programs are based on this text. Good mix of theory and implementation.

Golub, Gene H., 1984, Studies in Numerical Analysis, Mathematical Association of America, ISBN 0883851261. [Daniel Pick] This contains several outstanding essays from several numerical analysts, including Wilkinson's The Perfidious Polynomial, which explains why rootfinding of polynomials numerically is such a tricky problem. It gives an great introduction to the thinking of recent numerical analysts. [Amara Graps] All of the chapters are really good- my favorites are: "Fast Poisson Solvers" and "Multigrid Methods for Partial Differential Equations."

Kahaner, David; Moler, Cleve; Nash, Stephen, 1989, Numerical Methods and Software, Prentice Hall, ISBN 0-13-627258-4. An excellent book which touches on a variety of topics and makes use of the publicly available software like the QUADPACK and SLATEC libraries to illustrate the points. [Vijay Gupta]

Knuth, Donald E. 1981 The Art of Computer Programming: Seminumerical algorithms, 3rd edition, Addison-Wesley. Once was the reference; now a bit dated.

Lau, H. T., 1995, A Numerical Library in C for Scientists and Engineers CRC Press, ISBN 0-8493-7376-X. This book is basically a compilation of program listings, with a diskette containing source code. The listings are accompanied by brief overviews of the algorithms involved, and generally include references. There is no discussion of theory. While the text by Stoer & Bulirsch is at the theoretical end of the NA spectrum, this text is at the application end. Although the program calling parameters are well described, as far as I could see the programs contain no internal documentation whatsoever. Although this book is copyright 1995, the references contain one source dated 1992 (Press et al's volume), one source dated 1981 (NUMAL in Fortran), and one source dated 1980 (NUMAL in Algol). The remainder of the references are dated 1976 and earlier. It's not clear to me that this book offers anything over Press et al's text. Lau has far less discussion of theory and methodology, and while Press's internal documentation of programs may leave something to be desired, Lau's book has none whatsoever. [SJS]

Lau, Hang T., 2003, A Numerical Library in Java for Scientists and Engineers CRC Press, ISBN 1584884304. The book contains the source code on CD of a large numerical library in Java.

Mathews, John H. 1992, NUMERICAL METHODS: for Mathematics, Science & Engineering, Prentice Hall Source for the programs is available in several languages: Matlab, C, Fortran, Pascal,

Muller, Jean-Michel, 1997, Elementary functions, algorithms and Implementation, Birkhauser Boston.

Nash, John C., 1987, 1996, Nonlinear Parameter Estimation: an integrated system in BASIC.

Peters, Martin, 1997, Solving Problems in Scientific Computing Using Maple and MATLAB. All Maple and MATLAB programs can be obtained from: Peters text.

Petkovsek, Marko; Wilf, Herbert; Zeilberger, Doron, 1995, "A=B", AK PETERS, Ltd., ISBN 1-56881-063-6. [Donald Knuth] I'm especially pleased to see the appearance of this book, because its authors have not only played key roles in the new developments, they are also master expositors of mathematics. It is always a treat to read their publications, especially when they are discussing really important stuff. Science advances whenever an Art becomes a Science. And the state of the Art advances too, because people always leap into new territory once they have understood more about the old. This book will help you reach new frontiers.

Press, William H.; Teukolsky, Saul A.; Vetterling, William A.; Flannery, Brian P. 1992 Numerical Recipes in C, Second edition A long time standard practical text. A compendium of a wide variety of NA areas. Contains some good introductions to theory and overviews of algorithms. The bridge from algorithm overview to implementation is often missing. Some of the programs should be viewed with skepticism. Some are poorly documented, and some users have reported numerical problems with the various programs. [SJS] Their more recent C++ book appears to be simply a copy of the C book, with minimal C++ classes wrapped around the code.

The Numerical Recipes in C version may be downloaded for free.

Sedgewick, Robert. 1988, Algorithms, Second edition, Addison-Wesley.

Stewart, Ian. 1999, Notes on Matrix Algorithms I: Basic Decomposition, Notes on Matrix Algorithms II: Eigensystems. Siam Press. Parts may be available online at Ian Stewart's page.

Stoer, Josef; Bulirsch, Roland, Introduction to Numerical Analysis Springer-Verlag, New York, 1980, ISBN 0-387-90420-4. The classic NA text. A standard for graduate and upper undergraduate courses in NA. Covers a wide set of fields in depth. Strong theoretical orientation. [SJS]

Strang, Gilbert, 1988, Linear Algebra and It's Applications, Third Edition, Harcourt Brace, ISBN 0-15-551005-3. A well-written introduction to theory.

Strang, Gilbert and Borre, Kai, 1997, Linear Algebra, Geodesy, and GPS, Wellesley-Cambridge Press. The book has three closely connected parts. The first is Linear Algebra, which is the fundamental tool in positioning calculations. The second is Geodesy, which includes the correct weightings for observation errors and the development of least squares. The third is GPS, which we describe in detail at several levels : first the basic structure of the GPS system, then the algorithms that yield accurate positions from inaccurate pseudoranges, and finally the Kalman filtering (and "Bayes" filtering) that give superior accuracy in postprocessing a long series of observations.

Trefethen, Nick, and Bau, David, 1997, Numerical Linear Algebra, Siam.

Tyrtyshnikov, Eugene E, 1997, A Brief Introduction to Numerical Analysis. Birkhauser, Boston. Tyrtyshnikov writes: Without any doubt, there are many quite good and excellent books on the subject. But I know definitely that I did not realize this when I was a student. In this book, my first desire was to present those lectures that I wished I would have heard when I was a student.

Watkins, David S., 1991, Fundamentals of Matrix Computations John Wiley, ISBN 0-471-61414-9 More readable than Stoer & Bulirsch or Golub & Van Loan, and contains some implementation techniques not present in Golub & Van Loan. Has good descriptions of theory and implementations, and many implementations are covered as straightforward exercises. Not as wide a variety of fields as either Golub & Van Loan or Stoer & Bulirsch. [SJS]

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