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General/Basic Numerical Libraries:
aimLib -- a C++ mathematics library.
C++ Classes List -- several C++ classes for numerical analysis.
CCMATH -- a mathematics library coded in the C-language.
Cephes -- C language library for special functions of mathematical physics.
CERNLIB -- collection of general purpose programs for mathematical or data-handling problems.
C/Math Toolchest -- C/C++ library for scientific and engineering applications.
Chorale ToolBox -- numerical toolbox for Matlab/Octave.
CMLIB -- a collection of Fortran subroutine for mathematics and statistics.
Colt -- open source libraries for high performance scientific computing in Java.
CPML -- a replacement libm library for Alpha Linux with better performance.
GNUMATH(gnussl) -- a numerical mathematics library for scientific applications.
GSL (GNU Scientific Libaray) -- a collection of numerical routines for scientific computing.
Harwell Subroutine Library -- a suite of Fortran subroutines for scientific computation.
IMSL Math/Stat Libraries -- more than 900 FORTRAN numerical subroutines.
IMSL C Numerical Libraries -- math/statistics numerical subroutines for C programming.
jCrunch -- Java class libraries for robust and fast mathematical capabilities.
JNL -- a numerical library for Java.
LHC++ -- OO software library to replace CERNLIB.
libffm -- fast and free math routines for Linux/AXP.
Matpack
-- a C++ numerics and graphics library.
Multipack -- math Fortran routines linked to Python.
NAG C Libraries -- a large collection of algorithmic routines written in C.
NAG Fortran 77 Libraries -- Fortran 77 routines for mathematical and statistical computation.
NAG FL90plus and fl90 Fortran 90 Libraries -- Fortran 90 libraries.
PORT -- a collection of Fortran 77 routines for many traditional areas of mathematical software.
Scientific Math Library in C++ -- extensive collection of classes and routines.
Schelab -- a numerical analysis library for Scheme.
Scientific Python modules -- Python modules suitable for scientific research.
sl++ -- a C++ object oriented numerical library.
SLATEC -- common mathematical library.
SLICOT -- a general purpose basic control library.
TCBI NumLib -- templated library of numerical base calsses for basic data structures.
WNLIB -- a C subroutine library that contains numerous tools useful for programming pratice.
XSC -- language extensions for scientific computation for modern numerical software.
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Linear Algebra:
BLAS -- high quality building block routines for performing basic vector and matrix operations.
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Blitz++ -- a C++ template class library for scientific computing.
BPKIT -- a toolkit of block preconditioners for the iterative solution of linear systems.
C++ Matrix Class -- a simple, fast, efficient C++ Matrix class designed for scientists and engineers.
C++ Tensor Class -- a recursive class template definition for N-dimensional arrays.
C_EisPack
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CAM C++ Class Libraries -- graphics, matrix/vector and symbolic function classes.
Cheap Matrix
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Expokit -- software for computing small dense and large sparse matrix exponentials.
GISOLV
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GMRES/FGMRES -- implementation of GMRES iterative linear solvers.
IML++
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ISIS++ -- iterative scalable implicit solver in C++.
JAMA -- a basic linear algebra package for Java.
JAMPACK -- a class library for manipulating matrices in Java.
Iterative Linear Solvers for Finite Volume/Finite Difference Equations
LAPACK -- solving linear (includes least-square) equations, eigenvalue and singular value problems.
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LASPack -- solving large sparse systems of linear equations like those from solving PDE.

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LinAlg -- basic linear algebra and optimization C++ classlib.

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Matrona -- a small C++ class library with widely-used algorithms of matrix algebra.
MatView -- a scalable sparse matrix viewer.
Meschach
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MTL -- a high-performance generic component C++ library for matrix.
MV++ -- a small/efficient set of concrete vector and simple matrix C++ classes.
Newmat -- a C++ matrix library.
MultiScale Libaray
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SparseLib++ -- a C++ class library for efficient sparse matrix computations.
SVMT
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Template Numerical Toolkit (TNT) -- a numeric library for scientific computing in C++ (mainly linear algebra routines).
Differentiation/Integration:
ADIFOR -- automatic differentiation of Fortran codes.
BVP Software -- solving boundary value problem for ODE.
Cubpack++ -- a C++ package for automatic two-dimensional cubature.
DNA -- fast numerical solution of ODE in Maple.
FADBAD/TADIFF -- C++ package for automatic differentiation and Taylor expansion.
GELDA -- general linear differential algebraic equation solver.
Godess -- a generic ordinary differential equations solving system.
Integration Applet -- graphs user-supplied function and computes the area under the curve.
IVP Test Set -- Fortran 77 test set for initial value problems.
Numerical Integration -- collection of FORTRAN code for numerical computation of integrals.
Ode -- numerical solution of ordinary differential equations.
ODE++ -- a C++ class library for ordinary differential equations.
ODE Fortran Codes -- Fortran 77 programs for various ODE problems.
PCOMP -- automatic differentiation.
PseudoPack -- numerical differentiation by pseudospectral methods.
Scarab -- numerical integrator for ODE.
TAMC -- generate Fortran source for 1st order derivatives out of a Fortran routines.
TIDE -- a collection of C++ classes for differential equations.
XTC -- a tool for modeling spatial evolution equations (PDE, integro-differential equations).
Transform:
Optimized Libraries for Pentium Pro -- BLAS, FFT, Extended Precision, etc.
benchFFT -- a program to compare FFT implementations.
djbfft -- a fast code for small power-of-2 complex DFTs on a Pentium.
FFTW -- a C subroutine library for performing the Discrete Fourier Transform.
FXT -- C++ library for various transformation.
LiftPack -- a C library for the fast lifted wavelet transform (FLWT).
MultiScale Libaray -- routines for linear algebra, transformation and wavelet.
Radix-2 FFT -- radix-2 DFT of a sequence, or Fourier integral of an evenly tabulated function.
SPLIB -- spectral method routines.
Uvi_Wave -- a set of Wavelet Processing based functions implemented under Matlab and khoros 2.
WAILI -- a wavelet transform library which includes some basic image processing operations.
WavBox -- wavelet transforms and adaptive wavelet packet decompositions.
WaveLab -- library of MATLAB for wavelet analysis.
wvlt -- a small set of routines that allow the user to manipulate wavelets.
Arithmetics/Multi-Precision:
apfloat -- C++ arbitrary precision arithmetic package.
doubledouble -- implements approximately 30 decimal place floating point arithmetic.
FreeLIP -- a large integer package to factor the 129-digit number RSA-129.
GMP (GNU MP) -- a library for arbitrary precision arithmetic.
hfloat -- library for floating point numbers of extreme precision.
JUMP -- Java class library for unlimited precision computations.
LInteger -- a set of C++ libraries supporting multiple precision integers.
Mpexpr -- brings multiple precision math for Tcl.
MPFUN -- Fortran code for arithmetic computations to arbitrary numeric precision.
MPFUN++ -- a C++ implementation of MPFUN for calculation in arbitrary numeric precision.
Piologie -- library for arbitrary precision arithmetic for natural/integer/rational numbers.
SoftFloat -- implementation of IEC/IEEE Standard for Binary Floating-point Arithmetic.
XR -- an implementation of exact real arithematics.
Interpolation/Approximation:
C++ NURBS Library -- a C++ library for non-uniform rational B-splines curves and surfaces.
DT_NURBS -- a non-unofirm rational B-spline geometry subroutine library.
GUL -- geometry utility library for interpolation and approximation with NURBS surfaces.
kspline -- a library which provides spline functions.
NURBS Library -- Non-uniform rational B-splines library.
NURBS++ -- a C++ library to manipulate and create NURBS curves and surfaces.
NURBS Toolbox
-- routines for the creation, and manipulation of NURBS.
SCRIP -- a spherical coordinate remapping and interpolation package.
Siscat -- an object-oriented numerical library for approximation/interpolation of scattered data.
Snurbs -- simple NURBS libaray and a viewer.
Spherekit -- toolkit for spatial interpolation/comparison of spatial interpolation algorithms.
spline -- program for fitting a set of points using splines under tension.
Random Number Generator:
A Gaussian Random Number Generator -- with fast time-correlated feature.
ENT -- a pseudorandom number sequence test program.
Mersenne Twister -- a fast pseudorandom number generator.
Newran -- a C++ random number library.
pLab -- an object oriented system for generating and testing random numbers.
PRNG -- a C library for the generation of pseudorandom numbers.
RngPack -- a pseudorandom number generator package for Java.
RNPL -- rapid numerical prototyping language help scientists solve equations quickly.
Others:
ALFPACK -- Fortran subroutines for computing associated Legendre functions.
C++SIM -- an object-oriented simulation package written in C++.
Chaos Classes -- C++ classes for use in the study of chaotic dynamical systems.
CLAWPACK -- conservation laws software package.
CONTENT -- dynamical system software with differential equation solvers and tools.
cspX -- time series analysis algorithms for analyzing chaotic or regular data sets.
DsTool -- computational environment for dynamical systems.
Enclosing Ball Software -- calculates the smallest enclosing ball of a set of points or a set of balls.
Evolvuton and Other Software -- C++ software components for evolutionary computation and others.
FINDER -- pricing financial derivatives using low discrepancy methods.
GAIO -- a software package for the numerical analysis of dynamical systems.
IAsolver -- the Brandes interval arithmetic constraint solver implemented in Java.
LASSPTools -- numerical and graphical enhancements to Unix.
A Matlab Differentiation Matrix Suite -- solving differential equations by the spectral collocation method.
MCSim -- a package for Monte Carlo stochastic simulations.
MODFIT -- parameter estimation in Laplace transforms, ordinary/algebraic differential equations.
NAO -- objects for easy creation of numercial analysis software.
NumExp -- GTK+ based mathematical calculation program.
OAX -- a spacial objective analysis program.
Orderpack -- Fortran 90 code for general and specialized ordering problems.
PETE -- portable expression template engine.
The Polynomial Toolbox
-- a MATLAB toolbox for polynomials, polynomial matrices and their applications.
PROFIL/BIAS -- a C++ interval arithmetic class library.
PDEFIT -- parameter estimation in diffusion equations.
SHDOM -- spherical harmonic discrete ordinate method for atmospheric radiative transfer.
SLEIGN -- compute eigenvalues, eigenfunctions of regular/singular Sturm-Liouville (S-L) problems.
SYSFIT -- parameter estimation in systems of nonlinear dynamical equations.
TENSPACK -- nonlinear equation solving with tensor methods.
TONS -- to produce an environment for numerical calculations.
TRANSIENT -- solving arbitrary, nonlinear, parabolic PDEs in space and time.
UniCalc -- a universal solver for arbitrary algebraic systems of equations and inequlities.
XPP-Aut -- solving various equations arised in dynamical systems.
Also Check Out:
Algae -- a high-level interpreted language for numerical analysis.
C-Mix -- a program specializer for making faster C code.
CGAL -- a C++ software library of geometric data structures and algorithms.
CMAT -- an exact arithmetic matrix calculator program.
Emu/fdtd -- a 3D Maxwell's equation solver.
EiffelMath from ISE Eiffel -- object-oriented library for numerical and scientific computation.
ixlib -- C++ library with regular expressions, automatic arrays, garbage collection, matrix handling, planar geometry.
JavaView -- a 3D geometry viewer and numerical software library Java.
LCS -- Monte Carlo codes for simulating particles in an energy regime from TeV to thermal energies.
Matrix<LIB> -- a Matlab compatible C++ matrix class library.
SigLib DSP Library -- DSP, Signal and image processing software and libraries.
SILOON -- scripting interface languages for object-oriented numerics.
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