This is a list of notablenumerical libraries, which are libraries used in software development for performing numerical calculations. It is not a complete list of numerical libraries, but is instead a list of numerical libraries with articles on Wikipedia.
ALGLIB is an open source numerical analysis library which may be used from C++, C#, FreePascal, Delphi, VBA.
IMSL Numerical Libraries are libraries of numerical analysis functionality implemented in standard programming languages like C, Java, C# .NET, Fortran, and Python.
The NAG Library is a collection of mathematical and statistical routines for multiple programming languages (C, C++, Fortran, Visual Basic, Java and C#) and packages (MATLAB, Excel, R, LabVIEW).
BLOPEX (Block Locally Optimal Preconditioned Eigenvalue Xolvers) is an open-sourcelibrary for the scalable (parallel) solution of eigenvalue problems. Its object-oriented design allows easy portability.
FFTW (Fastest Fourier Transform in the West) is a software library for computing Fourier and related transforms.
IMSL Numerical Libraries are cross-platform libraries containing a comprehensive set of mathematical and statistical functions that can be embedded in a users application.
LabWindows/CVI is an ANSI C IDE that includes built-in libraries for analysis of raw measurement data, signal generation, windowing, filter functions, signal processing, linear algebra, array and complex operations, curve fitting and statistics.
Lis is a scalable parallel library for solving systems of linear equations and standard eigenvalue problems with real sparse matrices using iterative methods.
Trilinos, an effort to develop scalable (parallel) solver algorithms and libraries within an object-oriented software framework for the solution of large-scale, complex multi-physics engineering and scientific applications. A unique design feature of Trilinos is its focus on packages.
Armadillo is a C++ linear algebra library (matrix and vector maths), aiming towards a good balance between speed and ease of use. It employs template classes, and has optional links to BLAS and LAPACK.
Blitz++ is a high-performance vector mathematics library written in C++.
Eigen is a vector mathematics library with performance comparable with Intel's Math Kernel Library
Hermes Project: C++/Python library for rapid prototyping of space- and space-time adaptive hp-FEM solvers.
IML++ is a C++ library for solving linear systems of equations, capable of dealing with dense, sparse, and distributed matrices.
IT++ is a C++ library for linear algebra (matrices and vectors), signal processing and communications. Functionality similar to MATLAB and Octave.
LinBox is a C++ template library for doing exact computational linear algebra.
MTL4 is a generic C++ template library providing sparse and dense BLAS functionality. MTL4 establishes an intuitive interface (similar to MATLAB) and broad applicability thanks to Generic programming.
GNU Scientific Library (GSL) is a numerical library for C and C++ programmers. It is free software under the GNU General Public License. The library provides a wide range of mathematical routines such as random number generators, etc. There are over 1000 functions in total with an extensive test suite.
ILNumerics.Net high performance, typesafe numerical array classes and functions for general math, FFT and linear algebra, aims .NET/mono, 32&64 bit, script-like syntax in C#, 2D & 3D plot controls, efficient memory management
IMSL Numerical Libraries for .NET is a set of mathematical, statistical, data mining, financial and charting classes written in C#.
Measurement Studio is an integrated suite UI controls and class libraries for use in developing test and measurement applications. The analysis class libraries provide various digital signal processing, signal filtering, signal generation, peak detection, and other general mathematical functionality.
NMath by CenterSpace Software: numerical component libraries for the .NET platform, including signal processing (FFT) classes, a linear algebra (LAPACK & BLAS) framework, and a statistics package.
suanshu.net by Numerical Method Inc.: is a large collection of numerical algorithms including linear algebra, (advanced) optimization, interpolation, Markov model, principal component analysis, time series analysis, hypothesis testing, regressions, statistics, ordinary and partial differential equation solvers, and suanshu.
NLinear is a generic linear algebra toolkit in C# compatible with Silverlight.
Math.NET is an opensource initiative to build and maintain toolkits covering fundamental mathematics, targetting advanced but also every day needs of .Net developers. http://www.mathdotnet.com/
EISPACK is a software library for numerical computation of eigenvalues and eigenvectors of matrices, written in FORTRAN. It contains subroutines for calculating the eigenvalues of nine classes of matrices: complex general, complex Hermitian, real general, real symmetric, real symmetric banded, real symmetric tridiagonal, special real tridiagonal, generalized real, and generalized real symmetric matices.
IMSL Numerical Libraries are cross-platform libraries containing a comprehensive set of mathematical and statistical functions that can be embedded in a users application.
LINPACK is a software library for performing numerical linear algebra on digital computers. It was written in Fortran by Jack Dongarra, Jim Bunch, Cleve Moler, and Pete Stewart, and was intended for use on supercomputers in the 1970s and early 1980s. It has been largely superseded by LAPACK, which will run more efficiently on modern architectures.
Lis is a scalable parallel library for solving systems of linear equations and standard eigenvalue problems with real sparse matrices using iterative methods.
MINPACK is a library of FORTRAN subroutines for the solving of systems of nonlinear equations, or the least squares minimization of the residual of a set of linear or nonlinear equations.
NOVAS is a software library for astrometry-related numerical computations. Both Fortran and C versions are available.
Netlib is a repository of scientific computing software which contains a large number of separate programs and libraries including BLAS, EISPACK, LAPACK and others.
ARPACK is a collection of Fortran77 subroutines designed to solve large scale eigenvalue problems.
SHTOOLS is an archive of fortran 95 based software that can be used to perform (among others) spherical harmonic transforms and reconstructions, rotations of spherical harmonic coefficients, and multitaper spectral analyses on the sphere.
Apache Commons, is an open-source for creating reusable Java components. It has numerical packages for linear algebra and non-linear optimization.
JAMA, a numerical linear algebra toolkit for the Java programming language. No active development has taken place since 2005, but it still one of the more popular linear algebra packages in Java.
JHepWork, an open-source Java libraries for numerical calculations, data I/O and visualisation of scientific results. Used together with Jython.
JMSL Numerical Libraries, is a comprehensive set of mathematical, statistical, data mining, financial and 2D/3D charting classes.
Perl Data Language gives standard Perl the ability to compactly store and speedily manipulate the large N-dimensional data arrays which are the bread and butter of scientific computing.
NumPy, a library that adds support for the manipulation of large, multi-dimensional arrays and matrices; it also includes a large collection of high-level mathematical functions. NumPy serves as the backbone for a number of other numerical libraries, notably SciPy.
Sage Math is a large mathematical software application which integrates the work of nearly 100 free software projects and supports linear algebra, combinatorics, numerical mathematics, calculus, and more.
SciPy, a large library of scientific tools. Includes NumPy
ScientificPython, a library with a different set of scientific tools
JHepWork provides an interface to call numerical libraries using the Ruby programming language. The interfacing is done using JRuby (Ruby implemented in Java)
Others
XNUMBERS — Multi Precision Floating Point Computing and Numerical Methods for Microsoft Excel.
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