ru.algorithms

 
 - RU.ALGORITHMS ----------------------------------------------------------------
 From : Maxim Lanovoy                        2:463/1124.6   04 May 2002  20:47:06
 To : All
 Subject : Альтернатива NR
 -------------------------------------------------------------------------------- 
 

                     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 naive 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 author):
 
 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
 lectures 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 It's out-of-date in some areas, most notably in Least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. Diskette included.
 John H. Mathews, Numerical 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:
 ftp://ftp.mathworks.com/pub/books/mathews/c
 ftp://ftp.mathworks.com/pub/books/mathews/fortran
 ftp://ftp.mathworks.com/pub/books/mathews/pascal
 ftp://ftp.mathworks.com/pub/books/mathews/matlab
 NUMERICAL METHODS: Mathematica 3.0 Notebooks
 John H. Mathews and Russell W. Howell, COMPLEX ANALYSIS: for Mathematics and
 Engineering, Third Edition, 1997, ISBN 0-7637-0270-6.  With purchase of this
 book, free software is available.
 Zdzislaw Meglicki has posted the text for a course on advanced scientific
 computing at Indiana University.
 G. W. "Pete" Stewart posted the following in na-net:
 "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 service@siam.org."
 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 http://www.cs.umd.edu/~stewart/. I
 will be grateful for any comments, corrections, or suggestions.
 
 There are excellent texts and reference works that focus on narrow portions of
 the discipline of numerical analysis. Consider, for example:
 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 Norsett, 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. More 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).
 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 Computational Mathematics Subgroup, or obtain the Math77 and mathc90
 libraries of mathematical software directly. There is also a substantial amount 
 of software and information about software on-line.
 For one-of-a-kind computations, we recommend MATLAB (The MathWorks, Inc.).
 
  Revised: November 16, 2001
 ==============================================================================
 
 http://math.jpl.nasa.gov/nr/nr-alt.html
 WBR, Максим Лановой
 mailto: lanovoy(_at_)ln.ua
 
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