NUMERICAL SOFTWARE TOOLS
AND INFORMATION SOURCES
Nick Trefethen, October 2008
Software Repositories
Netlib (www.netlib.org)
NHSE = National HPCC
Software Exchange (www.nhse.org)
CALGO = Collected Algorithms
of the ACM (www.acm.org/pubs/calgo)
Fortran
90 Software Repository
(www.nag.co.uk/nagware/Examples.asp)
Information Portals
GAMS = NIST Guide to Available Mathematical Software
(gams.nist.gov)
MathSciNet
(klymene.mpim-bonn.mpg.de/mathscinet)
NA Digest weekly
online bulletin (www.netlib.org/na-digest-html)
Mathtools.net (www.mathtools.net)
Numerical Analysis Journals
(see also Oxford's e-Journals portal at
http://sfx7.exlibrisgroup.com/oxford/az)
ACM Transactions on Mathematical Software
IMA Journal of Numerical Analysis
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Mathematics of Computation
Numerische Mathematik
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
SIAM Review
ETNA = Electronic Transactions on Numerical Analysis
General-Purpose Libraries
NAG (www.nag.co.uk)
(F77 TOC)
IMSL (www.vni.com/products/imsl)
HSL Archive and
HSL 2004 (formerly "Harwell
Subroutine Library") (www.cse.clrc.ac.uk/nag/hsl/contents.shtml)
Numerical Recipes (www.nr.com)
GNU Scientific Library (www.gnu.org/software/gsl)
Wilkinson Prizes
DASSL
(and DASPK) = Differential Algebraic Equation Solver
(www.engineering.ucsb.edu/~cse/software.html)
ADIFOR
= Automatic Differentiation of Fortran (www-unix.mcs.anl.gov/autodiff/ADIFOR)
FFTW = Fastest
Fourier Transform in the West (www.fftw.org)
Triangle = 2D mesh generator
(www-2.cs.cmu.edu/~quake/triangle.html)
deal.II = finite element library
(www.dealii.org)
Symbolic and Extended Precision Computation
Maple (www.maplesoft.com)
Mathematica (www.wolfram.com)
Matlab Symbolic Toolbox
(www.mathworks.com/products/symbolic)
PARI/GP (pari.math.u-bordeaux.fr)
GMP = GNU Multiple Precision (www.swox.com/gmp/)
In Matlab:
help symbolic or doc symbolic,
help vpa or doc vpa
MATLAB for Gourmets
Scilab = open-source analog of Matlab
(www.scilab.org)
GNU Octave = another open-source analog of Matlab
(www.octave.org)
MATLAB Help Desk
(www.mathworks.com/access/helpdesk/help/helpdesk.shtml)
MATLAB Central file exchange
(www.mathworks.com/matlabcentral/fileexchange)
MATLAB Guide
by Higham and Higham (www.ma.man.ac.uk/~higham/mg)
Linear Algebra
Freely available software
(www.netlib.org/utk/people/JackDongarra/la-sw.html)
BLAS = Basic Linear Algebra Subprograms (www.netlib.org/blas)
EISPACK and
LINPACK (superseded by LAPACK)
LAPACK (www.netlib.org/lapack)
ScaLAPACK (www.netlib.org/scalapack)
ARPACK for
large eigenvalue problems (www.caam.rice.edu/software/ARPACK)
EigTool for nonsymmetric eigenvalues and pseudospectra
(www.comlab.ox.ac.uk/pseudospectra/eigtool)
Templates for the Solution
of Linear Systems
(www.netlib.org/linalg/html_templates/Templates.html)
Templates for the Solution
of Algebraic Eigenvalue Problems
(www.cs.utk.edu/~dongarra/etemplates/)
AZTEC =
A Massively Parallel Iterative Solver Library for Solving Sparse Linear Systems
(www.cs.sandia.gov/CRF/aztec1.html)
Matrix Market
(math.nist.gov/MatrixMarket)
In Matlab:
help sparfun or doc sparfun
Ordinary Differential Equations and Dynamical Systems
ODEPACK
(www.netlib.org/odepack)
DSTOOL
(mathlab.cit.cornell.edu/dyn_sys/dstool/dstool.html)
PHASER
(www.phaser.com)
In Matlab:
help funfun or doc funfun
Partial Differential Equations
CLAWPACK for
conservation laws
(www.amath.washington.edu/~claw)
PLTMG 2D elliptic PDE package
(www.scicomp.ucsd.edu/~reb/software.html)
FISHPAK fast Poisson
solvers (www.scd.ucar.edu/softlib/FISHPAK.html)
M-files
for spectral methods
(www.comlab.ox.ac.uk/nick.trefethen/spectral.html)
Comsol Multiphysics (= FEMLAB) (www.comsol.com)
Matlab PDE Toolbox
(www.mathworks.com/products/pde)
PDELAB
(www.cs.purdue/edu/research/cse/pdelab)
DIFFPAK
(www.diffpack.com)
In Matlab:
help pde or doc pde
Optimization
Optimization
Technology Center
(www.ece.northwestern.edu/OTC)
NEOS Guide
(www-fp.mcs.anl.gov/otc/Guide)
Decision Tree for Optimization
Software (plato.la.asu.edu/guide.html)
Matlab Optimization Toolbox
(www.mathworks.com/products/optimization)
In Matlab:
help optim or doc optim
Other Numerical Topics
Top 500 Supercomputer Sites
(www.top500.org)
MGNET = Multigrid/multilevel/multiscale...
Network (casper.cs.yale.edu/mgnet/www/mgnet.html)
Mesh
Generation & Grid Generation on the Web
(www-users.informatik.rwth-aachen.de/~roberts/meshgeneration.html)
Spline bibliography
(www.cs.wisc.edu/~deboor/bib/bib.html)
Digital Library of Mathematical Functions
(dlmf.nist.gov)
wavelet.org
(www.wavelet.org)
Overview of
Iterative Linear System Solver Packages (www.netlib.org/utk/papers/iterative-survey)
CFD Packages
CFD Online
(www.cfd-online.com/Resources)
FLUENT (www.fluent.com)
CFX (www.ansys.com/Products/cfx.asp)
Statistics
Statlib
(lib.stat.cmu.edu)
SPSS (www.spss.com)
S-Plus (www.insightful.com)
R = open-source analog of S-Plus
(www.r-project.org)
SAS (www.sas.com)
In Matlab:
help stats or doc stats
Computation on the Web
NEOS =
NEOS Server for Optimization (www-neos.mcs.anl.gov)
NetSolve/GridSolve
(www.cs.utk.edu/netsolve)
Encylopedia of
Integer Sequences
(www.research.att.com/~njas/sequences)
Inverse Symbolic Calculator
(oldweb.cecm.sfu.ca/projects/ISC/ISCmain.html)
Chef's Choice
Schwarz-Christoffel
toolbox for MATLAB (www.math.udel.edu/~driscoll/SC)
chebfun system for Matlab computing with continuous functions on [-1,1]
(www.comlab.ox.ac.uk/chebfun)
High-Performance Computing
PETSc =
Portable, Extensible Toolkit for Scientific Computation
(www-unix.mcs.anl.gov/petsc)
hpc netlib =
High-Performance Netlib
(www.nhse.org/hpc-netlib)
MPI =
Message-Passing Interface (for distributed memory computers) (www-unix.mcs.anl.gov/mpi)
OpenMP
(for shared memory computers) (www.openmp.org)
ATLAS =
Automatically Tuned Linear Algebra Software
(math-atlas.sourceforge.net)
OSC = Oxford Supercomputing Centre
(www.osc.ox.ac.uk)
Graphics and Visualization
IRIS Explorer
(www.nag.com/welcome_iec.asp)
DX = IBM Visualization
Data Explorer (www.research.ibm.com/dx)
AVS = Advanced Visual Systems (www.avs.com)
Fieldview (www.ilight.com) (this and next two especially good for CFD)
Ensight (www.ceintl.com)
Visual3/pV3
(raphael.mit.edu/haimes.html)
In Matlab:
help graphics or doc graphics