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Topic: FAQ: Numerical Analysis and Associated Fields Resource Guide (1/1)
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Steve Sullivan

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Registered: 12/7/04
FAQ: Numerical Analysis and Associated Fields Resource Guide (1/1)
Posted: Dec 14, 1996 11:19 AM
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Archive-name: num-analysis/faq/part1
Last-modified: 1996 December 14

q10. FAQ: Numerical Analysis & Associated Fields Resource Guide

Welcome! My intent here is to provide reviews of software, texts,
and other resources instead of simply a listing. My experience is
that for someone looking for a package or system, reviews by previous
users can be a lifesaver.

If you have any suggestions, comments, or contributions please send
them to me at: sullivan@mathcom.com

Other reviews would be most welcome! If you use a mathematical
package or set of programs and would care to write one to twenty
sentences on it, please let me know. If you have a favorite text
or two you'd like to recommend, please let me know.

Sigh, and now the legalities ...

The information contained in this document is believed to be true,
but no guarantees of accuracy are made, and there is no liability
of any sort for any consequences of its use.

This document may be copied and/or reproduced providing that:
* the use is for non-commercial purposes only, and
* all copies contain this copyright notice:
* Copyright 1995-6 S. J. Sullivan


See:
* q20, "NA FAQ: Introduction"
* q30, "NA FAQ: Overview of Recent Additions"
* q40, "NA FAQ: Table of Contents"
* q50, "NA FAQ: Acknowledgements"


Steve Sullivan
sullivan@mathcom.com

Mathcom, Inc.
8555 Hollyhock St., Lafayette, CO 80026 USA


=========================================================================

q20. NA FAQ: Introduction

Where to find this FAQ:

On the web:
http://www.indra.com/~sullivan/q10.html Mathcom

This FAQ is usually available from MIT's rtfm and its mirrors:
ftp://rtfm.mit.edu/pub/usenet/news.answers/num-analysis/faq/part1 MIT's rtfm

If not, a compressed (with gzip) version is at:
ftp://ftp.mathcom.com/mathcom/nafaq.txt.gz Mathcom ftp

A mirror site in Germany, courtesy of Jens Burmeister
(jb@numerik.uni-kiel.de), is:
http://www.numerik.uni-kiel.de/faqs/tda/q10.html Mirror in Germany

Abbreviations used in this document:



NA Numerical Analysis

### Denotes "to be filled in later". This is work in progress,
and probably always will be.

[] Reviews are associated with the name of the reviewer in brackets.
Those reviews marked [SJS] are by myself.

[author] indicates text taken from a package documentation.

10^12 10 to the power 12. In Fortran, that's 10**12;
in C that's pow(10,12).

x(i) the i'th element of vector x. In C, that would be x[i].


Instead of the normal question/answer form, this FAQ is organized
as an outline ... hopefully, you'll find your questions answered here.


=========================================================================

q30. NA FAQ: Overview of Recent Additions



q125.11, "Matlab to C++ Compiler and C++ Matrix Class Library"
MAT<LIB>, a Matlab Compatible C++ Matrix Class Library.


q260.2.7, "QMG"
[author]: QMG is free software for fully automatic unstructured finite
element mesh generation in two and three dimensions. It can generate meshes
for complex polyhedral domains with nonmanifold features.

q265.1, "Optimization, Linear and Non-Linear Programming"
NEOS Guide to Optimization Software

q260.6, "Books and References for PDE and FEM"
Books by Wolfgang Hackbusch.

q520.1, "Comparative Reviews on Symbolic Algebra Packages"
Michael Wester's page on comparative reviews of symbolic
algebra packages.

q570, "Constraints"
University of New Hampshire Constraint Computation Center


As well as numerous other updates.


=========================================================================

q40. NA FAQ: Table of Contents


* q10, "FAQ: Numerical Analysis & Associated Fields Resource Guide"
* q20, "NA FAQ: Introduction"
* q30, "NA FAQ: Overview of Recent Additions"
* q40, "NA FAQ: Table of Contents"
* q50, "NA FAQ: Acknowledgements"
*
* q105, "What is Numerical Analysis?"
* q110, "Indices of NA Software on the Net"
* q112, "Indices of Commercial NA Software"
* q115, "Libraries of NA Software on the Net"
* q120, "NA Packages on the Net"
* q125, "Commercial NA Libraries and Packages"
* q135, "Newsgroups for NA"
* q140, "Professional Societies for NA"
* q145, "Electronic Newsletters for NA"
* q150, "Electronic Journals for NA"
* q155, "Online Preprints for NA"
* q160, "Miscellaneous Web Sites for NA"
* q165, "Books, With and Without Software, for NA"

Specialized Subfields Within Numerical Analysis
* q205, "Dense (Non-Sparse) Linear Algebra Systems"
* q207, "Sparse Linear Algebra Systems"
* q210, "Random Number Generators (RNGs)"
* q215, "Function Evaluation"
* q220, "Finding Roots"
* q230, "Curve Fitting, Data Modelling, Interpolation, Extrapolation"
* q240, "Transforms (FFT, etc) and digital signal processing (DSP)"
* q245, "Wavelets"
* q250, "Integration and Ordinary Differential Equations (ODEs)"
* q253, "Stochastic Differential Equations"
* q255, "N-Body and Particle Simulation"
* q260, "Partial Differential Equations (PDEs) and Finite Element Modeling (FEM)"
* q265, "Operations Research: Minimization, Optimization"
* q270, "Computational Geometry"
* q285, "Graphics and Scientific Visualization"
* q290, "Miscellaneous NA Software"

Associated Fields
* q505, "Probability and Statistics"
* q510, "Chaos Theory (Nonlinear Dynamics)"
* q520, "Symbolic Algebra"
* q530, "Cryptography (Cryptology)"
* q540, "Fractals"
* q550, "Neural Networks"
* q560, "Discrete algorithms"
* q570, "Constraints"
* q580, "Genetic Algorithms"
* q590, " Simulated Annealing"

Teaching and Academic Software
* q800, "Teaching and Academic Software"



===========================================================================


q50. NA FAQ: Acknowledgements

Many thanks to all those who've given their time and advice
in creating this FAQ, including:

Bob Berman berman@FERMAT.macsyma.com
Ronald F Boisvert boisvert@cam.nist.gov
Ted Brown tbrown@tekotago.ac.nz
John Chandler jpc@a.cs.okstate.edu
Luiz Henrique de Figueiredo lhf@csgrs6k1.uwaterloo.ca
Bill Frensley frensley@utdallas.edu
Pawel Gora gora@if.uj.edu.pl
Amara Graps agraps@netcom.com
Vijay Gupta gupta@acsu.Buffalo.edu
Doug Hart hart@de01.denver.waii.com
Albert Hines ahines@howmet.com
Charles Knechtel doug@scn.org
Zdislav V. Kovarik kovarik@mcmail.cis.McMaster.CA
Dave Linder dwl@apmaths.uwo.ca
George Marsaglia geo@stat.fsu.edu
Pierre Maxted pflm@star.maps.susx.ac.uk
Allen Mcintosh mcintosh@bellcore.com
Sean O riordain sor@inrets.fr
Daniel Pfenniger pfennige@scsun.unige.ch
Daniel Pick pick@lune.math.tau.ac.il
Brian Ripley ripley@stats.ox.ac.uk
Ramin Samadani ramin@leland.Stanford.EDU
Robert Schneiders robert@Informatik.RWTH-Aachen.DE
Peter Somlo somlo@zeta.org.au
Tim Strotman tim.strotman@sdrc.com
N. Sukumar n-sukumar@nwu.edu
Stephen Vavasis vavasis@CS.Cornell.EDU
Dave Watson watson@maths.uwa.edu.au

Many thanks also to the organizers of the many services
listed herein - Netlib, the NIST guide, NA-Net, CAIN, the NASA
Graphics site, and numerous other indices and informative web pages.


===========================================================================

q105. What is Numerical Analysis?

NA is the union of theoretical and computational investigation into
the computer solution of mathematical problems. NA generally includes
those problems involving continuous functions of real or complex
variables, as opposed to solely discrete variables and functions.

The mixing of theoretical and computational concerns leads to
a strong emphasis on algorithms: what are the time and memory
usage properties of a certain algorithm? What errors are introduced
by an algorithm?

The compuational aspects of NA usually take place within
the scope of floating-point arithmetic, and are implemented on
machines ranging from super-computers through PCs to hand-calculators.
The theoretical aspects extend into fields such as Calculus,
Differential Equations, and Analysis. The field of Linear Algebra
is so often used to model physical systems that the theoretical
study of Linear Algebra is in itself often considered to be
NA at work.

Primary areas of theoretical concern in NA are:
* global/local error bounding
* stability of algorithms
* rates of convergence of algorithms

Primary areas of computational concern in NA are:
* roundoff error
* global/local error and its tolerance
* time and memory requirements of computation
* High Performance Computing (HPC)
* parallel computing
* architechture/platform specific details.


===========================================================================


q110. Indices of NA Software on the Net

For indices of packages oriented towards symbolic algebra,
see q520, "Symbolic Algebra".


The NIST Guide to Available Mathematical Software (Formerly called GAMS)

http://gams.nist.gov/ NIST Guide to Mathematical Software
or telnet to: gams.nist.gov

[SJS]:
Maintained by National Institute of Standards and Technology (NIST)
An index and server for a wide variety of mathematical
software, including most of netlib (see q115.1, "Netlib").
Much of the software is in Fortran. If you prefer to speak C++ or C,
see q160.1, "C++ Resources", and q115.2, "Fortran, C, and f2c".

[Ronald Boisvert]:
The main focus is on fine-grained software components, e.g.
subroutines, although information about some larger packages are
included. As of November 1995, nearly 10,000 components from more
than 90 packages have been cross-indexed using a detailed
tree-structured problem classification system. Both freely available
software (from netlib or developed at NIST) and commercial packages
(used by NIST) are indexed, although source code is available only for
non-commercial software.

===================================

q112. Indices of Commercial NA Software

A large list of commercial NA products may be found at:
http://www.cray.com/PUBLIC/APPS/DAS/ Cray

The Directory of commercial software, by International Computer
Programs, Inc., is at:
http://www.icp.com/softinfo/ ICP

Finally, for packages oriented towards symbolic algebra,
see q520, "Symbolic Algebra".

===========================================================================

q115. Libraries of NA Software on the Net

Libraries are collections of source code, and source code packages.
Much of the code is in Fortran. If you prefer to speak C++ or C,
see q160.1, "C++ Resources", and q115.2, "Fortran, C, and f2c".

The main library by far is q115.1, "Netlib".
For statistical software, the best resource is q115.3, "Statlib".
Other libraries are q115.4, "NCAR's Mathematical and Statistical Libraries"
and q115.5, "Hensa Unix Parallel Archive".

* q115.1, "Netlib"
* q115.2, "Fortran, C, and the f2c Translator"
* q115.3, "Statlib"
* q115.4, "NCAR's Mathematical and Statistical Libraries"
* q115.5, "Hensa Unix Parallel Archive"
* q115.6, "Modula-3 NA Library"
* q115.7, "Forth Numerical/Scientific Library"
* q115.8, "Eiffel Numerical/Scientific Library"
* q115.9, "Lisp Numerical/Scientific Libraries"

===========================================================================

q115.1. Netlib
NetLib is probably the world's largest repository of numerical
methods programs. It is located at Oak Ridge National Laboratory,
Knoxville, Tennessee, and at AT&T Bell Laboratories, Murray Hill, NJ.


email: send message "help" to either:
netlib@ornl.gov
netlib@research.att.com

http://www.netlib.org Netlib main
http://www.netlib.org/netlib/netlib_faq.html Netlib FAQ
http://www.netlib.org/master/expanded_liblist.html Netlib index
ftp://netlib.att.com/netlib Netlib via ftp

Netlib mirrors:

http://www.netlib.no/ Netlib in Norway
or email to: netlib@nac.no

http://www.hensa.ac.uk/ftp/mirrors/netlib/master/ Netlib in England
or email to: netlib@ukc.ac.uk

http://elib.zib.de/netlib/master/readme.html Netlib in Germany
or:
http://elib.zib-berlin.de/netlib Netlib in Germany
or email to: anonymous@elib.zib-berlin.de

ftp://draci.cs.uow.edu.au/netlib/ Netlib in Australia
or email to: netlib@draci.cs.uow.edu.au

Netlib in Taiwan: email only: netlib@nchc.edu.tw


Some gems of netlib:

Machine/architecture dependant Basic Linear Algebra Subroutines
(BLAS) are the keystone of Netlib.

LAPACK, in Fortran 77, is the modern replacement
of EISPACK, LINPACK, etc.

CLAPACK is a C version of LAPACK. See the Caution on
Using Arrays in q115.2, "Fortran, C, and f2c".

LAPACK++ is a C++ version of, sadly, only a subset of LAPACK.
LAPACK++ is work in progress, and hopefully the full
functionality of LAPACK will be supported soon.

ScaLAPACK is for distributed memory machines.




===================================


q115.2. Fortran, C, and the f2c Translator

For C++ and C resources, see q160.1, "C++ Resources".

Most of the programs in netlib are in Fortran. However, netlib
contains an excellent Fortran-to-C conversion utility, f2c.
While f2c produces working C code, it is visually complex
and ugly. Using f2c on a large package like LAPACK can require
a good deal of time to get all the options correct.
Fortunately, LAPACK has already be converted to C: see CLAPACK.

The utility f2c can also be invoked by email. Send email
to netlib@research.att.com, with the subject "execute f2c",
and body containing the non-confidential Fortran program to be converted.
But the email option is of use only for very small, simple programs,
since a resulting C program of any size must be linked with the
f2c libraries. Usually one will have to download the f2c package
anyway to generate the libraries. Generally it's easier
to download the f2c package, build the libraries and the
f2c conversion program, and do the conversion locally.

CAUTION: Programs created by f2c conversion use parameter passing
conventions different from most C or C++ programs. Their
callers must create the appropriate parameters before using them.
See the file f2c.ps in the f2c distribution.
A good description of this issue may also be found in
the "readme" file for clapack in netlib.


===================================

q115.3. Statlib

Statlib is a huge repository of statistics related software and info.
Probability, statistics, random variables, distribution functions.

http://lib.stat.cmu.edu/ Statlib at CMU
ftp://lib.stat.cmu.edu Statlib via ftp
email: send message "send index" to statlib@lib.stat.cmu.edu


===================================


q115.4. NCAR's Mathematical and Statistical Libraries

NCAR's libraries contain some overlap with netlib.

http://http.ucar.edu/SOFTLIB/mathlib.html NCAR


===================================

q115.5. Hensa Unix Parallel Archive

General info, software, articles, etc., on parallel computing.

http://www.hensa.ac.uk/parallel/environments/pcn/ Hensa
Note: this web server can be very slow!



===================================

q115.6. Modula-3 NA Library

http://www.eskimo.com/~hgeorge/ Modula-3 NA
and pick the link to m3na.
This is a libraried collection of numerical analysis routines written
in Modula-3. Includes linear algebra, roots, ffts, and a bit
of statistics.


===================================

q115.7. Forth Numerical/Scientific Library

http://www.taygeta.com/fsl/sciforth.html Skip Carter's Forth Library at Taygeta

===================================

q115.8. Eiffel Numerical/Scientific Library

http://www.eiffel.com/products/math.html Commercial Eiffel library at I.S.E.

===================================

q115.9. Lisp Numerical/Scientific Libraries


http://euler.bd.psu.edu/lispstat/ statistical tools.

http://setosa.uwaterloo.ca/~ftp/Quail/features.html U. Waterloo

http://eksl-www.cs.umass.edu/research/clip-clasp-overview.html instrumentation and statistical analysis packages

ftp://ftp.cs.cmu.edu/user/ai/lang/lisp/code/math/0.html CMU's library




===========================================================================


q120. NA Packages on the Net

Packages generally include an NA library and an interpretive
language for a front end.

Also see q520, "Symbolic Algebra", for free symbolic algebra packages.

* q120.1, "Octave"
* q120.2, "RLaB"
* q120.3, "Scilab"
* q120.4, "Tela"
* q120.6, "Medal"
* q120.7, "Euler"
* q120.8, "Prophet"
* q120.9, "Yorick"
* q120.10, "PETSc"

===================================

q120.1. Octave

http://bevo.che.wisc.edu/octave.html Octave
ftp://www.che.wisc.edu/pub/octave Octave via ftp

[Dave Lindner]: Octave is considered the closest-to-Matlab
of the Matlab clones.

[author]:
Octave is a high-level language, primarily intended for
numerical computations. It provides a convenient command line
interface for solving linear and nonlinear problems
numerically.

Octave can do arithmetic for real and complex scalars and matrices,
solve sets of nonlinear algebraic equations, integrate functions over
finite and infinite intervals, and integrate systems of ordinary
differential and differential-algebraic equations.

The Octave distribution includes a 200+ page Texinfo manual.
Two and three dimensional plotting is fully supported using gnuplot.

The underlying numerical solvers are currently standard
Fortran ones like Lapack, Linpack, Odepack, the Blas,
etc., packaged in a library of C++ classes.

===================================

q120.2. RLaB

http://www.eskimo.com/~ians/rlab.html RLaB
ftp://csi.jpl.nasa.gov/pub/matlab/RLaB RLaB via ftp
ftp://evans.ee.adfa.oz.au/pub/RLaB RLaB via ftp in Australia

[author]:
Rlab is an interactive, interpreted scientific programming
environment. Rlab is a very high level language intended to provide
fast prototyping and program development, as well as easy
data-visualization, and processing.

Rlab is not a clone of languages such as those used by tools like
Matlab or Matrix_X/Xmath. However, as Rlab focuses on creating a good
experimental environment (or laboratory) in which to do matrix math,
it can be called "MATLAB-like" since the programming language
possesses similar operators and concepts.

===================================

q120.3. Scilab

http://zenon.inria.fr/Logiciels/SCILAB-eng.html Scilab
ftp://ftp.inria.fr/INRIA/Scilab Scilab via ftp

[Dave Lindner]: Scilab is another good Matlab clone.

[author]:
Scilab is a high-level language for numerical computations
in a user-friendly environment. It features:
Elaborate data structures (polynomial, rational and string
matrices, lists, multivariable linear systems,...).
Sophisticated interpreter and programming language with
Matlab-like syntax.
Hundreds of built-in math functions (new primitives can easily be
added).
Stunning graphics (2d, 3d, animation).
Open structure (easy interfacing with Fortran and C via online
dynamic link).

Many built-in libraries :
* Linear Algebra (including sparse matrices, Kronecker
form, ordered Schur,...).
* Control (Classical, LQG, H-infinity, ...).
* Signal processing.
* Simulation (various ode's, dassl,...).
* Optimization (differentiable and non-differentiable, LQ solver).
* Metanet (network analysis and optimization).
Symbolic capabilities through Maple interface.

===================================

q120.4. Tela

http://www.geo.fmi.fi/prog/tela.html Tela
ftp://ftp.funet.fi/pub/sci/math/tela Tela via ftp

General NA package with graphics, linear algebra, FFT, etc.
Is this another Matlab clone?

[author]:
It is mainly targeted for prototyping large-scale
numerical simulations and doing pre- and postprocessing for them, and
it replaces a compiled language like C++ or Fortran in this respect.
The feature set is therefore biased to operations needed in partial
differential equation solvers.




===================================

q120.6. Medal

ftp://excel2.uwaterloo.ca/pub Medal

Apparently there is also available is a commercial version of Medal:
Email : medal@excel2.uwaterloo.ca

[author]:
MEDAL is a novel expert system development environment which is integrated
within a control system design environment, and which supports a tight
coupling of symbolic and numeric processing. MEDAL supports the development
of coupled systems in engineering and science.

MEDAL (Matrix and Expert system Development Aid Language) is an interactive
program. The language syntax of MEDAL is similar to the popular MATLAB
(Matrix Laboratory) language. MEDAL retains all of the main features of
MATLAB, including the MATLAB syntax and M-files.
In addition, MEDAL includes an integrated expert system shell for the
development of knowledge-based systems which can perform
sophisticated numeric calculations. Hence, the additional
expert system predicates extends the MATLAB command language syntax.
Also, MEDAL supports a rich set of data structure for representing
objects in the programming environment. Knowledge can be
represented using facts, rules and frames.

Main features of MEDAL :
------------------------
* interactive computing environment ( command-drive )
* language syntax and user-interface similar to MATLAB
* all basic MATLAB-type of matrix functions are provided
* flexible 2-D graphics
* design of linear control systems
* packed matrix representation, as well as regular matrices
* automatic loading of M-files ( open philosophy )
* build-in knowledge base development facilities (expert shell )
* knowledge repesentation : rules, facts, objects ( frames )
* simple knowledge base of the Systematic Design Approach is included
* runs on Sun Sparc workstations (X-window), PC (DOS), DEC (Ultrix)

References:

(1) Pang, G.K.H.,``Knowledge-based Control System Design'', in
Recent Advances in Computer-Aided Control Systems Engineering,
Jamshidi, M and Herget, C.J. (ed.), Elsevier Science Publishers, 1992.

(2) Pang, G.K.H., ``A Knowledge Environment for an Interactive Control
System Design Package'', Automatica, Vol. 28. No. 3, pp. 473-491, May 1992.

===================================

q120.7. Euler

ftp://am.ku-eichstaett.de/pub Euler via ftp

[author]:
EULER started as a MatLab clone. It is now a program, which can handle
real, complex and interval numbers and matrices, has a 2D/3D graphics, a
builtin modern programming language (extension of MatLab's), an exact
scalar product, and the Windows 95 version can call functions in an
external DLL. The OS/2 and Windows versions interact nicely with the GUI,
and have a notebook style interface.

The Unix version is free, the OS/2 version free for educational use, and
the Windows version cheap shareware.

These features make EULER an ideal tool for the tasks such as
* Inspecting and discussing functions of one real or complex
variable.
* Viewing surfaces in parameter representation.
* Linear algebra and eigenvalue computation.
* Testing numerical algorithms.
* Solving differential equations numerically.
* Computing polynomials.

===================================

q120.8. Prophet

http://www-prophet.bbn.com/ Prophet
ftp://www-prophet.bbn.com Prophet via ftp
email: prophet-info@bbn.com

[author]:
Prophet is an NIH-sponsored Unix workstation software package for life
science computing. Prophet includes tools for data management,
statistical analysis, curve fitting, data graphing, mathematical
modeling, and genetic sequence analysis.

One of PROPHET's greatest assets is its new graphical
user interface . Employing the latest advances in software
technology, PROPHET lets you store,
analyze and present Data Tables, Graphs, Statistical Analyses and
Mathematical Modeling, and Sequence Analyses with high-resolution
graphics and multiple windows. Anyone, from the computer-naive to the
computer-sophisticate, can learn to use it quickly and effectively.
PROPHET is a National Computing Resource for Life Science Research
sponsored by the National Center for Research Resources of the
National Institutes of Health.

Unfortunately, prophet is distributed in binary form only.
It is large: it takes something like 65 MB disk space.

===================================

q120.9. Yorick
wuarchive.wustl.edu: /languages/yorick/yorick-1.2.tar.gz
sunsite.unc.edu: /pub/languages/yorick/yorick-1.2.tar.gz
sunsite.unc.edu: /pub/Linux/apps/math/matrix/yorick-1.2.tar.gz
netlib.att.com: /netlib/env/yorick-1.2.tar.gz
netlib2.cs.utk.edu: /env/yorick-1.2.tar.gz

[author]
Yorick is an interpreted language. It has:
* A C-like language, but without declarative statements. Operations
between arrays require no explicit loops, which accounts for
Yorick's high speed. Scientific computing and numerical analysis
are the goals of most Yorick sessions.
* An X window system interactive graphics package.
* A library of functions written in the Yorick language.
Because Yorick can read either text or binary files, it can be used
"out of the box" as a pre- and post-processor for most existing
physics simulation programs.

As a pre-processor, you can write a Yorick program that produces
complicated input files for a simulation. These might be based on
output from other programs, or might require evaluation of complicated
functions or involve a lot of repetition.

As a post-processor, Yorick allows you to compare the results of
several simulations or to analyze results of a single simulation in
ways you did not forsee when you ran it.


===================================

q120.10. PETSc
ftp://info.mcs.anl.gov/pub/petsc PETSc by ftp
http://www.mcs.anl.gov/petsc/petsc.html PETSc by www

[author]:
Portable, Extensible Toolkit for Scientific Computation (PETSc).
PETSc provides many tools for the parallel (and uniprocessor),
numerical solution of PDEs that require solving large-scale, sparse
nonlinear systems of equations. PETSc includes nonlinear and linear
equation solvers that employ a variety of Newton techniques and Krylov
subspace methods. In addition, PETSc provides several parallel sparse
matrix formats, including compressed row, block compressed row, and
block diagonal storage.

PETSc is fully usable from Fortran, C and C++, and runs portably on
on most UNIX systems. PETSc uses MPI for all parallel communication.

One of the unique features of PETSc is that it enables the
application programmer to easily and efficiently assemble parallel
vectors and sparse matrices. Users can create complete application
programs for the parallel solution of nonlinear PDEs without writing
much explicit message-passing code themselves.

In addition, PETSc is designed to facilitate extensibility. Thus,
users can incorporate customized solvers and data structures when
using the package.



===========================================================================

q125. Commercial NA Libraries and Packages

Commercial libraries and packages tend to merge, so I've combined
them in one category. Typically a commercial product contains:
* a library of numerical routines
* graphics routines
* an interactive interpreted language

Many symbolic algebra packages also contain NA packages.
For info on these packages, see q520, "Symbolic Algebra".

An good article on commercial software is:
Braham, Robert. "Math & Visualization: new tools, new frontiers",
IEEE Spectrum 32, 11 (November 1995), p. 19-36.
The article contains tables comparing large number of commercial products.
There is no mention of the many excellent free products though.

* q125.1, "NAG"
* q125.2, "IMSL and PVWAVE"
* q125.3, "Matlab and Simulink"
* q125.4, "WavBox"
* q125.5, "CraySoft Libraries"
* q125.6, "IDL"
* q125.7, "Comparison of IDL and Matlab"
* q125.8, "Mlab"
* q125.9, "Gauss"
* q125.10, "MathViews"
* q125.11, "Matcom: Matlab to C++ Compiler"

===================================


q125.1. NAG

http://www.nag.co.uk:70/ NAG in England
http://www.nag.com/ NAG in USA

[SJS]: Numerical, symbolic, statistical, and visualization libraries in
Fortran 77, Fortran 90, C, Pascal, Ada, and parallel machine versions.
High performance Fortran 90 and Fortran 77 compilers.

NAG Ltd (The Numerical Algorithms Group)

Wilkinson House
Jordan Hill Road
OXFORD
OX2 8DR
UK
Tel: +44 1865 511245

NAG Inc
1400 Opus Place
Suite 200
Downers Grove
IL 60515-5702
USA
Tel: +1 708 971 2337


===================================

q125.2. IMSL and PVWAVE

http://www.vni.com/indexall.html Visual Numerics, Inc.

[SJS]: IMSL is a set of routines in C, C++, and Fortran
libraries for general NA, statistics and graphics.
PVWAVE is a visual programming environment built on top of IMSL.

Visual Numerics, Inc.
IMSL and Stanford Graphics Products
9990 Richmond Avenue, suite 400
Houston, Texas 77042-4548
USA
Tel: 800-222-4675
Tel: 713-784-3131
FAX: 713-781-9260
e-mail: marketing@houston.vni.com

Visual Numerics, Inc
PV-WAVE Products Division
6230 Lookout Road
Boulder, Colorado 80301
USA
Tel: 800-447-7147
Tel: 303-530-9000
FAX: 303-530-9329
info@boulder.vni.com

[author]:
* Comprehensive Mathematical Functionality
* integration and differentiation
* transforms
* differential equations
* linear systems
* interpolation and approximation
* eigensystem analysis
* optimization
* special functions
* basic matrix/vector operations
* nonlinear equations
* utilities

* Extensive Statistical Functionality
* basic statistics
* tests of goodness-of-fit
* time series analysis and forecasting
* analysis of variance
* regression
* nonparametric statistics
* correlation
* random number generation
* cluster analysis
* categorical and discrete data analysis
* probability distribution functions and inverses
* factor analysis
* utilities

* Exponent Graphics includes:
* Presentation quality graphs for application development
* Application program interface provides easy access to either
FORTRAN or C
* Two function calls can automatically produce one of over 30
different plot types.
* Maximum flexibility for modifying plot chacteristics
* Powerful interactive editing and customization tools
* CGM, PostScript, HPGL and other device drivers
* Support for popular graphics accelerators and output systems
* Full Windows-based online documentation with hypertext links

PV-WAVE is a software environment for solving problems requiring the
application of graphics, mathematics, numerics and statistics to data
and equations.
PV-WAVE uses an intuitive fourth generation language (4GL) that
analyzes and displays data as you enter commands. With it you can
perform complex analysis, visualization, and application
development quickly and interactively.

Robust integrated graphics, numerics, data I/O, and data management
has made PV-WAVE the number one selling Visual Data Analysis software
family.

PV-WAVE and the IMSL numerical and statistical routines, which are
seamlessly integrated in PV-WAVE Advantage, are being used by more
than 300,000 technical professionals on workstations worldwide.


===================================

q125.3. Matlab and Simulink

http://www.mathworks.com/ Mathworks

The MathWorks, Inc.
24 Prime Park Way
Natick, MA 01760-1500
(508) 653-1415

For a comparison of Matlab and IDL, see
q125.7, "Comparison of IDL and Matlab".

[SJS]: Matlab is an interactive general NA package, including graphics.
A huge variety of "toolboxes" are available, both from the
vendor and on the net, for various specialized NA areas:
control systems, neural nets, optimization, symbolic math,
and on and on.
Simulink is modeling, simulation, and system analysis tool.

[author]:
MATLAB is a technical computing environment for high-performance
numeric computation and visualization. MATLAB integrates numerical
analysis, matrix computation, signal processing, and graphics in an
easy-to-use environment where problems and solutions are expressed
just as they are written mathematically - without traditional
programming.

MATLAB has evolved over a period of years with input from many users.
In university environments, it has become the standard instructional
tool for introductory courses in applied linear algebra, as well as
advanced courses in other areas. In industrial settings, MATLAB is
used for research and to solve practical engineering and mathematical
problems. Typical uses include general purpose numeric computation,
algorithm prototyping, and special purpose problem solving with matrix
formulations that arise in disciplines such as automatic control
theory, statistics, and digital signal processing (time-series
analysis).

MATLAB also features a family of application-specific solutions that
we call toolboxes. Very important to most users of MATLAB, toolboxes
are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment in order to solve particular classes of
problems. Areas in which toolboxes are available include signal
processing, control systems design, dynamic systems simulation,
systems identification, neural networks, and others.

SIMULINK is a tool for modeling, analyzing, and simulating an
extraordinarily wide variety of physical and mathematical systems,
including those with nonlinear elements and those which make use of
continuous and discrete time.

As an extension of MATLAB, SIMULINK adds many features specific to
dynamic systems while retaining all of MATLAB's general purpose
functionality.

Using SIMULINK, you model a system graphically, sidestepping much of
the nuisance associated with conventional programming.

===================================


q125.4. WavBox

http://www.wavbox.com/ Wavbox
email: info@wavbox.com

A wavelet Toolbox for Matlab.
[author]:
A software toolbox for wavelet transforms and adaptive
wavelet packet decompositions with new satisficing search algorithms.
Requires Matlab.



===================================

q125.5. CraySoft Libraries

http://www.cray.com/PUBLIC/product-info/craysoft/CS_home_txt.html Cray product info
http://www.cray.com/ Cray main
http://www.cray.com/craysoft/ Craysoft main
email: crayinfo@cray.com

Corporate Headquarters:
Cray Research, Inc.
655 Lone Oak Drive
Eagan, Minnesota 55121
(800) 289-2729 or (612) 683-3030,

[author]
Fortran 90 compilers and NA library for Cray, Sparc,
Macintosh, and Windows environments.
* Seismic migration
* Structural analysis
* Financial modeling
* Decision support analysis
* General scientific
* Computational chemistry
* Computational physics
* Intelligence, signal and image processing
* Electronic simulation


===================================

q125.6. IDL

Research Systems Inc.

http://www.rsinc.com/ Research Systems, Inc.
Research Systems, Inc.
2995 Wilderness Place
Boulder, CO 80301 USA
Phone: 303-786-9900
email: info@rsinc.com

For a comparison of IDL and Matlab, see
q125.7, "Comparison of IDL and Matlab".

IDL binaries are available at:
ftp://ftp.rsinc.com/pub/idl Research Systems, Inc.
ftp://boulder.colorado.edu/pub/idl U. of Colorado
ftp://ftp.Germany.EU.net/shop/CreaSo/IDL Germany

Following are two sets of comments on IDL:
1. By Pierre Maxted
2. By Amara Graps

================

1. Comments by Pierre Maxted

I find that IDL is good for "playing" with data. This works well for
astronomers who seem to end up always wanting to do something a little
different to last time to data that always has slightly different quirks
everytime. I also find that it is a rather easy language in which to
write my own routines. This is probably because I can start with
interactive IDL to get the feel for what the data is like and what I want
to do with it - this then becomes a simple batch file which can be turned
into a routine if the procedure is useful - this seems to be a natural
way to develop things. These libraries of routines are what makes IDL
really powerful in my opinion. I found that adding the astronomy user's
library to IDL was like adding wheels to a car. I would recommend to
anyone considering using IDL to find out what libraries are out
there (e.g. starting at the IDL WWW homme page).

Whatever you add to the FAQ, make one point clear - calling IDL a fancy
plotting package is like calling a Formula 1 racing car good for picking
up the kids from school - IDL can do plotting, but that is not its
strength.

Well, I agree that the hard copy manuals are rather opaque but Version 4
of IDL has online help (Hyperhelp) that is rather good - especially since
it had text searching capabilites so that you can go straight to the bit
you need (usually).


================

2. Comments by Amara Graps

Following is an excerpt of comments by [Amara Graps]:
For the full text of her review, please see:
http://www.amara.com/papers/miscpap.html Amara Graps' Papers
ftp://ftp.amara.com/papers/IDL_Matlab.txt Amara Graps' Papers via ftp

If you install IDL without a valid license, you will get IDL's
7 minute demo mode. This mode is designed for users who are
considering buying the package.

IDL is a vector-based language that makes it easy to manipulate arrays
and matrices. I've done testing comparing IDL speed to
Fortran in various actions, and IDL was as fast as a Fortran program for
the IDL array computations where loops were removed (i.e., when
using implicit loops in IDL instead of explicit FOR statments).

The scientific functions and procedures that come with IDL are often all
that scientists need. In addition, there are net archives
containing contributed routines. The archives at
John Hopkins and at Goddard are especially good (see below).

The language, for the most part is "open", i.e. you can see the
text of any particular procedure or function, in case you doubt the
technique, or want to modify it. Some functions and procedures are
black-box, intrinsic functions or procedures, but not nearly as many as
Matlab (see below) are.

Most work in IDL is done at the command line level. However, IDL supplies
rudimentary "widgets" to wrap a GUI around your procedures and
functions. You can create buttons, menus, scrollboxes etc.

Three-d plotting is currently not very well documented, and the way that
IDL does it is very convoluted. Other users and I have complained about
it, and I think RSI are taking steps to better document how to do it.

Image procesing and animation is pretty slick.
If you need to do "slicing and dicing" of a volume, in a way like
Spyglass Dicer, IDL has a really great widget routine to do it.
The IDL plots are high quality enough to use in initial journal
submissions.

RSI's support (writing to support@rsinc.com) is pretty good, I
usually get responses within 24-34 hours. You have to pay yearly technical
support costs, though- about $200 year (don't remember exactly how much).
The Usenet group: comp.lang.idl-pvwave has some smart programmers giving
answers if you don't want to pay for the IDL technical support. RSI
usually doesn't answer questions on that newsgroup (they have a company
policy against promoting IDL there because it's shared by two products:
IDL and PVWave).

I've never liked the IDL documention very much. The information that you
need probably *is* in the manuals, but it's somewhat hard to find (the
manuals are organized in a wierd way). [Note, however, the comments
by Pierre Maxted above].

The anonymous ftp sites below contain public domain IDL code.


http://fermi.jhuapl.edu/www/s1r/idl/idl.html JHU/APL/S1R IDL library
ftp://fermi.jhuapl.edu/pub/idl JHU/APL/S1R IDL library via ftp

NASA IDL Astronomy User's Library, run by Wayne Landsman:
http://idlastro.gsfc.nasa.gov/homepage.html NASA IDL Astro Library
ftp://idlastro.gsfc.nasa.gov/pub NASA IDL Astro Library via ftp

ftp://iuesn1.gsfc.nasa.gov IUE RDAF library at NASA
ftp://cetus.colorado.edu/pub IUE RDAF library at U. of Colorado

ftp://ftp.astro.psu.edu/pub/nefftp/icur ICUR Spectral Analysis Software

ftp://legacy.gsfc.nasa.gov/rosat/software/idl IDL ROSAT software

ftp://ftp.sma.ch/pub/idlmeteo IDLmeteo library

ftp://eos.crseo.ucsb.edu/pub/idl ESRG library


Hal Mueller has a Digital U.S. Map browser based on images
created by Ray Sterner at Johns Hopkins University using IDL:
http://www.zilker.net/~hal/apl-us// Map browser

E. Loren Buhle, Jr. Ph.D. made a page on AVS IN MEDICAL TREATMENT
PLANNING which also discusses IDL:
http://archive.xrt.upenn.edu/0h/buhle/manuscripts/avs94_paper.html Medical Treatment Planning



===================================

q125.7. Comparison of IDL and Matlab

Following is an excerpt of a paper by [Amara Graps]:
For the full text of her review, please see:
http://www.amara.com/papers/miscpap.html Amara Graps' Paper
ftp://ftp.amara.com/papers/IDL_Matlab.txt Amara Graps' Paper via ftp

IDL is a package that began life as an image-processing utility that has
grown to be a general-purpose numerical analysis tool. Matlab started as
a numerical analysis package that now includes [at extra cost] image
processing tools. Now the two have a similar scientific data-analysis
environment, with capabililties to build GUI programs and do very robust
data analysis.

(Note: all prices are approximate October 1995 prices - SJS)
They each cost about the same: ~$1500 for Mac and PC versions and more for
Unix (~4000 -- single user to $15,000 -- unlimited number of users).

Matlab is popular among education institutions because it has exceptional
educational discounts. If you are an academic, Matlab can be had for
$495 and each toolbox only $195. My NASA colleagues thought that
MathWorks "nickled- and-dimed" them with the costs of the Toolkits (like
the signal processing toolkit), but given what you get, it probably
isn't that unreasonable.

IDL seems to be more widespread in the NASA communities probably because
the original developer used several spacecraft teams (Pioneer Venus and
Voyager) as test beds for the IDL software.

IDL is more of a true programming language. Matlab has scripts and
functions and no way to explicitly type a variable. IDL has programs,
procedures, and functions and a language syntax sort of like a cross
between Fortran, Pascal, and APL. If you have programmed in Fortran
before, then the syntax will be a snap to learn. Matlab's syntax is much
more compact than IDL's. For example: x = transpose(y) in IDL is x=y' in
Matlab.

Matlab has many more built-in, intrinsic functions than IDL.
MatLab has many optional Toolkits, such as a Signal Processing
Toolkit and an Image Processing Toolkit, which are libraries
of more intrinsic functions.

Reading and writing files, and handling formats such as GIF,
PICT, GDF, and custom formats, seems much easier in IDL than MATLAB.
Handling directories is difficult in MATLAB when run on non-unix
machines.

Matlab has more types of graph types than IDL, and handling
colors is simpler than IDL. However, I found most
other Matlab graphical programming non-intuitive. It uses a system where
each element in a graph is an "object." These objects can have
sub-objects. So to change an element in a graph, say the axis color, you
have to first find the object (a "get" function), and then set it to the
color you want. IDL has system variables storing all graphics elements
which can be easily changed. One can also customize a graph upon making
the graph, with a keyword.

IDL's technical support is pretty good, but Matlab's is better. Post
a question on comp.soft-sys.matlab and either a developer, the company
president, or a tech support person will respond that day. You can call
them, too, but it's not a toll-free call.

===================================

q125.8. Mlab

http://www.civilized.com/MLAB.htmld/ Civilized Software

Civilized Software, Inc.
7735 Old Georgetown Rd. #410
Bethesda, MD 20815
U.S.A.
1-301-656-4714
1-301-656-1069 fax
Email: csi@civilized.com


[author]:
MLAB, (for Modeling LABoratory), is a program for interactive
mathematical and statistical modeling. MLAB was originally developed
at the National Institutes of Health. It includes curve-fitting,
differential equations, statistics and graphics as some of its major
capabilities.

===================================


q125.9. Gauss

email: info@aptech.com
Aptech Systems has a web page on Gauss at:
http://www.netaxis.qc.ca/~j.breslaw Aptech Systems

Aptech Systems, Inc., Tel: (206) 432-7855, Fax: (206) 432-7832
23804 South East Kent-Kangley Road
Maple Valley, WA 98038 USA
(206) 432-7855

[author]:
The GAUSS Mathematical and Statistical System is available for IBM PCs and
compatibles as well as UNIX workstations

As a complete programming language, the GAUSS system is both
flexible and powerful. Immediately available to the GAUSS user is a wide
variety of statistical, mathematical and matrix handling routines. Powerful
data handling capabilities including a data loop allow transformations in a
data set by directly using variable names inexpressions. This greatly
simplifies data transformations and makes for shorter more readable programs.
GAUSS can be used in either command mode(interactively) or in edit mode. In
command mode; one-line commands, or small screen-resident programs, can be
issued and the results of calculations seen immediately. In edit mode you
can write complex programs and store them in files.

GAUSS has over 400 functions built in, including LINPACK and EISPACK
routines.

===================================


q125.10. MathViews

http://www.mathwizards.com MathViews

[author] MathViews for Windows is matlab look-alike. It
has a full set of linear algebra and signal processing
functionality. It provides easy access to: matrix and linear
algebra, digital signal processing, instrument control, image
processing, time series analysis, data visualization and
waveform display and editing.
MathViews is highly compatible with the matlab syntax and will
execute most matlab m-files with no changes.
We also have WaveTool.
WaveTool is an interactive software tool for creating, editing
and analyzing captured waveshapes. Waveforms can be created
using any combination of drawing, math expressions (matlab
syntax), insertion from a library of waveforms or data values
pasted from other applications such as Microsoft Excel.

===================================


q125.11. Matlab to C++ Compiler and C++ Matrix Class Library

http://www.mathtools.com Mathtools
or email: info@mathtools.com

[author]:
MATCOM V2 is a Matlab(R) to C++ compiler. MATCOM creates MEX files
and standalone C++ applications, with royalty free distribution.
MATCOM translates Matlab code to C++, which is compiled by your
optimizing C++ compiler. The resulting code runs significantly faster
than the original interpreted source.
Prior knowledge of C++ is not necessary to use MATCOM. The compilation
is fully automated by a smart project manager.
Fully functional, time limited evaluation version of MATCOM V2 can be
downloaded freely from the MathTools web site.

MAT<LIB>, a Matlab Compatible C++ Matrix Class Library,
is designed for development of advanced
scientific high-level C++ code. Evalution version of the MAT<LIB>
can be downloaded from the home page noted above.
The library includes Complex math, Binary and unary operators,
Powerful indexing capabilites, Signal processing, File I/O, Linear
algebra, String operations and Graphics. Over 300 mathematical
functions are included in MAT<LIB>.
MAT<LIB> supports matrices of doubles, floats, ints and chars
mixed in the program. Images can be stored in matrices of chars,
using 1/8 memory storage. On many applications, where 8 digits of
precision are sufficient, float-precision matrices can save half
the memory usage. Memory allocation and de-allocation is managed
automatically.



===========================================================================

q135. Newsgroups for NA


Newsgroups related to numerical analysis are:


sci.math.num-analysis The primary group for NA issues.

sci.math.symbolic Covers symbolic algebra: Mathematica, Maple,
Macsyma, Derive, Reduce, Mcad, etc.

comp.soft-sys.math.mathematica: Devoted to Mathematica.

sci.op-research Covers operations research, linear programming,
non-linear programming.

sci.stat.math Covers probability and statistics.

sci.math Covers a broad range of mathematical subjects, at
levels from trivial to advanced.

sci.math.research Covers advanced mathematics, and
is generally theoretical as opposed to applied.



===========================================================================

q140. Professional Societies for NA

* q140.1, "The (AMS) American Mathematical Society"
* q140.2, "(SIAM) The Society for Industrial and Applied Mathematics"
* q140.3, "ACM, Inc. (Association for Computing Machinery)"
* q140.4, "IEEE The Institute of Electrical and Electronic Engineers"

===================================

q140.1. The (AMS) American Mathematical Society

http://www.ams.org/ AMS
email: ams@math.ams.org

General organization information, preprint titles, pointers to
other preprint servers and net resources. Also includes:

MathDoc, the document delivery service offered by the AMS, provides
copies of original journal, collection and conference proceedings
articles from publications covered by Mathematical Reviews, Current
Mathematical Publications, and the MathSci database. This costs
roughly US$14. per ten pages, as of October 1995.

MathSciNet is a searchable database available on the World Wide Web.
It is based on the data in Mathematical Reviews and Current
Mathematical Publications, leading publications that catalog and
review research literature in mathematics. This costs roughly
US$5500. per year, as of October 1995.

===================================

q140.2. (SIAM) The Society for Industrial and Applied Mathematics

http://www.siam.org/ SIAM
email: siam@siam.org

General organizational information, tables of contents
of SIAM journals, and recently accepted articles.
Society for Industrial and Applied Mathematics
3600 University City Science Center
Philadelphia, PA 19104-2688
(215) 382-9800

Journals include:
SIAM Scientific Computing
SIAM Matrix Analysis
SIAM Control and Optimization

===================================

q140.3. ACM, Inc. (Association for Computing Machinery)

http://acm.org/ ACM
email: ACMHELP@acm.org

General organizational information, info on journals and conferences.
Of particular interest are:

Transactions on Mathematical Software (TOMS)
http://www.acm.org/pubs/toms/ ACM TOMS

Collected Algorithms of the ACM (CALGO)
Software can be found in netlib (toms directory); see q115.1, "Netlib".

SIGNUM (Special Interest Group in Numerical Mathematics)
http://www.acm.org/sig_hp/SIGNUM.html ACM SIGNUM

ACM Headquarters
One Astor Plaza
1515 Broadway
New York, New York 10036
212-869-7440

===================================

q140.4. IEEE The Institute of Electrical and Electronic Engineers

http://www.ieee.org IEEE
email: member.services@ieee.org

General organizational information, journals, books, conferences.
Tel: (800) 678-IEEE
Tel: (212) 705-7900

===========================================================================

q145. Electronic Newsletters for NA

http://www.netlib.org/na-net/na_home.html NA-Net
http://www.netlib.org/na-digest/topics NA-Net Index

email: nanet@na-net.stanford.edu

[author]:
The NA-Net is a system developed to serve the community of numerical
analysts and other researchers. The Na-Net provides two independent
databases and a weekly digest to its members. The Email Database is
the electronic mail address of each of its members, and is capable
of forwarding mail to them. In addition, this database serves as the
distribution list for the NA Digest (see below). The White Pages
Database is basically a directory service. It provides a way to
exchange personal information among its members. Contained in the
database are phone numbers, postal mailing addresses, research
interests, affiliations, etc. The NA Digest is a way to provide its
members with a weekly collection of articles on topics related
to numerical analysis and those who practice it. To get on the
mailing list for the digest and enter yourself in their database,
you can use email or the World Wide Web. Take advantage of this very
useful service!

===========================================================================

q150. Electronic Journals for NA

Indices of Journals

See the large list of online journals, and other resources,
at Penn State's Mathematics web site.

http://www.math.psu.edu/OtherMath.html Penn State Mathematics

See also:
http://rattler.cameron.edu/swjpam/ The Southwest Journal of Pure and Applied Mathematics



===================================

BIT

http://math.liu.se/BIT/ BIT
BIT emphasizes numerical methods in approximation, linear algebra, and
ordinary and partial differential equations, but also publishes papers
in areas such as numerical functional analysis and numerical
optimization.

===================================

ETNA (Electronic Transactions in Numerical Analysis).

http://etna.mcs.kent.edu/ ETNA
An online peer reviewed journal. Keyword searching.
Most documents are postscript and may be downloaded.
Started in 1993. Indexes only itself.

===================================

EJDE, The Electronic Journal of Differential Equations

http://ejde.math.swt.edu/ EJDE
A purely on-line peer-reviewed journal.

===================================

The Electronic Journal of Linear Algebra

http://gauss.technion.ac.il/iic/ela/ Electronic J. of Linear Algebra

===================================

New York Journal of Mathematics

http://nyjm.albany.edu:8000/nyjm.html NY J. of Mathematics
Appears more abstract than applied. Started in 1994. Indexes only itself.


===========================================================================

q155. Online Preprints for NA

General
See the listings for professional societies, especially the AMS,
in q140, "Professional Societies for NA".

Springer-Verlag
Preprints: See the Springer-Verlag preprint service via email.
Not free.
http://www.springer.de/server/services.html Springer Verlag

Virtual Library Math Journals Preprints
http://euclid.math.fsu.edu/Science/Preprints.html Virtual Lib Math Jnls Preprints
Links to numerous organizations offering preprints.


===========================================================================

q160. Miscellaneous Web Sites for NA

See also:
* q160.1, "C++ Resources for NA"
* q160.2, "Math FAQ"


Caltech guide to mathematics resources
http://www.ama.caltech.edu/resources.html Caltech Guide to Math Resources
Good collection of pointers to quality sites.

Penn State's Math Guide
http://www.math.psu.edu/OtherMath.html Penn State Math Guide
Huge site with information on many fields within mathematics.

U. C. Berkeley
gopher://math.berkeley.edu U.C. Berkeley gopher site (large)
ftp://math.berkeley.edu /pub U.C. Berkeley ftp site (large)
http://math.berkeley.edu/ U.C. Berkeley ftp site (small)
Berkeley has a large gopher & ftp site, including courseware, pointers
to inet libraries, lecture notes, seminars, and software.

Indiana University: Mathematical Computing Resources Guide
http://www.indiana.edu/~statmath/mathsites.html Indiana University.
An excellent large site.


The World-Wide Web Virtual Library: Mathematics
http://euclid.math.fsu.edu/Science/math.html Virtual Lib: Mathematics
Specialized fields (topology, cryptography, optimization, etc),
academic departments, miscellaneous math societies and institutes,
pointers to commercial software, newsgroups, nice collection
of preprints pointers, electronic journals

U. Tennessee Knoxville Mathematics Archives WWW Server
http://archives.math.utk.edu/ U. Tenn Knoxville Math Archives

MathSoft's Favorite Mathematical Constants
http://www.mathsoft.com/asolve/constant/constant.html Mathsoft Constants
Constants and algorithms for their generation.

Tomasz Plewa's list of www sites for numerical methods
http://tonic.physics.sunysb.edu/docs/num_meth.html Plewa's NA page, USA
http://www.math.psu.edu/dna/num_methods.html Plewa's NA page, USA
http://zar.unizar.es/www/num_meth.html Plewa's NA page, Spain
http://www.labyrinth.net.au/~ctrans/tomasz.html Plewa's NA page, Australia

Amara Graps' list of science links
http://www.amara.com/science/science.html Amara Graps' list

A Catalog of Mathematics Resources on WWW and the Internet
http://mthwww.uwc.edu/wwwmahes/files/math01.html Catalog of Math Resources
By M. Maheswaran, University of Wisconsin Marathon Center.
Another large site, with a sizeable section on Applied Mathematics.

Altug Koker's list of simulation software
http://piranha.eng.buffalo.edu/simulation/comp.simulation/FAQ.html Simulation Software
(See his Q15.). Contains pointers to software for:
aerospace, automotive, chemistry / biotechnology, graphics and imaging,
electronics / electrical engineering, petroleum

The Yahoo server's index of Mathematics topics.
http://www.yahoo.com/Science/Mathematics Yahoo's Math index
Includes commercial products, conferences, journals, and various
subfields of mathematics, primarily in applied mathematics.


Scientific Applications on Linux Web Page
http://lusk1.mines.edu/hjjou/linux_old.html Scientific Apps on Linux
Contents:
* Commercial Scientific Software
* MatLab Alike and Related Packages
* Mathematics and Statistics
* Finite or Boundary Element
* Numerical Analysis
* Signal, Communication, Data and Image Processing/Visualization
* CAD, Graph, Drawing and Modelling Tools
* Scientific Data Plotting Packages
* Scientific Data Plotting Libraries
* General Purpose Graphic Libraries
* Word Processing, Typesetting And Office Software
* X-Window GUI Construction
* Misc Scientific Packages or Libraries and Links
* Other Links


For a wide variety of links to mathematical and scientific software, see:
http://www-ocean.tamu.edu/~baum/linuxlist-m.html S. Baum's site

===================================

q160.1. C++ Resources for NA

Ajay Shah's index of resources for NA in C or C++
http://www.math.psu.edu/FAQ/numcomp-free-c.txt Ajay Shah's C++ Resources
ftp://usc.edu/pub/C-numanal/numcomp-free-c.gz Ajay Shah's C++ Resources via ftp
ftp://ftp.math.psu.edu/pub/FAQ/numcomp-free-c Ajay Shah's C++ Resources via ftp

The Object-Oriented Numerics Page
http://monet.uwaterloo.ca/blitz/oon.html Object-Oriented NA
Pointers to C++ libraries and classes.

Also see q590, "Skip Carter's Home Page".

Also see Joerg Arndt's web page on FFT code, at
q240, "Transforms (FFT, etc) and digital signal processing (DSP)"

===================================

q160.2. Math FAQ

The sci.math FAQ by Alex Lopez-Ortiz is a good reference for
many mathematical questions. It is more oriented towards
pure mathematics than NA.
http://daisy.uwaterloo.ca/~alopez-o/math-faq/math-faq.html Alex Lopez-Ortiz's list
ftp://rtfm.mit.edu/pub/usenet-by-group/news.answers/sci-math-faq/ Alex Lopez-Ortiz's list via ftp

===========================================================================

q165. Books, With and Without Software, for NA

See also specific subject areas in this FAQ
at q80, "NA FAQ: Table of Contents".


Petkovsek, Marko; Wilf, Herbert; Zeilberger, Doron. 1995
"A=B"
Publisher: AK PETERS, Ltd., 289 Linden Street, Wellesley, MA 02181
Telephone to (617) 235-2210. $39.
ISBN 1-56881-063-6
[Donald Knuth] Science is what we understand well enough
to explain to a computer. Art is everything else we do.
During the past several years an important part of
mathematics has been transformed from an Art to a
Science: No longer do we need to get a brilliant insight in order to
evaluate sums of binomial coefficients, and many similar formulas that
arise frequently in practice; we can now follow a mechanical procedure
and discover the answers quite systematically.

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.


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?"


Golub, Gene H.; Van Loan, Charles F. 1989
Matrix Computations, Second edition
Johns Hopkins, Baltimore
ISBN 0-8018-3739-1
Telephone: 410-516-6900

[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."


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]


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]


Kahaner, David; Moler, Cleve; Nash, Stephen. 1989
Numerical Methods and Software
Prentice Hall, Englewood Cliffs, NJ
ISBN 0-13-627258-4
Telephone: 800-947-7700

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
Seminumerical algorithms, 2nd 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, Boca Raton, FL
ISBN 0-8493-7376-X
Telephone: 407-994-0555

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 is poor, Lau's book has none whatsoever. [SJS]



Mathews, John H. 1992
NUMERICAL METHODS: for Mathematics, Science & Engineering
Prentice Hall, Englewood Cliffs, NJ
ISBN 0-13-624990-6 and
ISBN 0-13-625047-5

Source for the programs is available in several languages:
ftp://ftp.mathworks.com/pub/books/mathews/matlab Matlab (ftp)
ftp://ftp.mathworks.com/pub/books/mathews/c C (ftp)
ftp://ftp.mathworks.com/pub/books/mathews/fortran Fortran (ftp)
ftp://ftp.mathworks.com/pub/books/mathews/pascal Pascal (ftp)
ftp://ftp.wri.com/pub/Publications/BookSupplements/Mathews-1996/ Mathematica (ftp)
http://www.wri.com/MathSource/Publications/BookSupplements/Mathews-1996/0207-874 Mathematica (http)


Press, William H.; Teukolsky, Saul A.; Vetterling, William A.;
Flannery, Brian P. 1992
Numerical Recipes in C, Second edition
Cambridge University Press, Cambridge and New York
ISBN 0-521-43108-5 Text
ISBN 0-521-43720-2 Example book
ISBN 0-521-43714-8 PC diskette, 5.25 inch
ISBN 0-521-43724-5 PC diskette, 3.5 inch
ISBN 0-521-43715-6 Mac diskette, 3.5 inch
Telephone: 212-924-3900, 800-872-7423

Seperately purchasable diskette contains C source code.
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. The programs should be viewed with
some skepticism. They are often poorly documented, and some users
have reported numerical problems with t



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