List of numerical analysis software

Listed here are a number of computer programs used for performing numerical calculations:
 * APL (programming language) is a language designed for array manipulation that is used for a wide variety of scientific, engineering, and actuarial analysis.
 * acslX is a software application for modeling and evaluating the performance of continuous systems described by time-dependent, nonlinear differential equations.
 * Baudline is a time-frequency browser for numerical signals analysis and scientific visualization.
 * COMSOL Script for numerical computations and interactive partial differential equation solving with the finite element method; uses MATLAB-compatible syntax. Optionally connects to COMSOL Multiphysics.
 * DADiSP is a commercial program focused on DSP that combines the numerical capability of MATLAB with a spreadsheet like interface.
 * Euler (software) EULER is a powerful numerical laboratory with a programming language that can handle real, complex and interval numbers, vectors and matrices. It can produce 2D/3D plots.
 * Expensive Desk Calculator (historical), written for the TX-0 and PDP-1 in the late 1950s or early 1960s.
 * FlexPro is a commercial program for interactive and automated analysis and presentation of mainly measurement data. It supports many binary instrument data formats and has its own vectorized programming language.
 * Frink, a programming language and calculating tool which tracks units of measure through all calculations.
 * FreeMat, an open-source MATLAB-like environment with a GPL license.
 * GAUSS, a matrix programming language for mathematics and statistics.
 * GNU data language, a free compiler designed as a drop-in replacement for IDL.
 * GNU Octave can generally run scripts written for recent versions of MATLAB; has an active user community. (free software, GNU GPL license).
 * GNU Scientific Library, a popular, free numerical analysis library for C and C++.
 * GNU Multi-Precision Library is a library for doing arbitrary precision arithmetic.
 * IDL programming language, a commercial interpreted language based on FORTRAN with some vectorization. Widely used in the solar physics, atmospheric sciences and medical communities.  The GNU data language is a free alternative.
 * IGOR Pro, a software package with emphasis on time series, image analysis, and curve fitting. It comes with its own programming language and can be used interactively.
 * ILNumerics.Net typesafe numerical array classes and functions for general math and linear algebra, aims .NET/mono, script-like syntax in C#, 2D & 3D plot controls
 * IML++ is a C++ library for solving linear systems of equations, capable of dealing with dense, sparse, and distributed matrices.
 * IMSL Numerical Libraries are libraries of numerical analysis functionality implemented in standard programming languages like C, Java, C# .NET, and Fortran.
 * IMTEK Mathematica Supplement is an open source (GNU GPL license) collection of tutorials and packages for numerical calculations.
 * IT++ is a C++ library for linear algebra (matrices and vectors), signal processing and communications. Functionality similar to MATLAB and Octave.
 * JAMA, a numerical linear algebra toolkit for the Java programming language
 * JScience, an open-source (multiple licenses) Java API for performing numerical calculations and data storage among other things.
 * LabVIEW offers both textual and graphical programming approaches to numerical analysis. Its text-based programming language MathScript utilizes .m file script syntax providing some compatibility with MATLAB, COMSOL Script, FreeMat, GNU Octave, O-Matrix, Rlab, Scilab, and Sysquake.
 * LAPACK++, a C++ wrapper library for LAPACK and BLAS
 * Lush is an object-oriented programming language based on LISP for large-scale numerical and graphic applications
 * Macsyma, a general-purpose computer algebra system, which has a free GPL-licensed version called Maxima.
 * Maple, a general-purpose commercial mathematics software package.
 * Mathcad offers a WYSIWYG interface and the ability to generate publication-quality mathematical equations.
 * Mathemagix, is an open source (GNU GPL license) general-purpose mathematics software package.
 * Mathematica offers numerical evaluation, optimization and visualization of a very wide range of numerical functions. It also includes a programming language and computer algebra capabilities.
 * MATLAB is a widely used program for performing numerical calculations. It comes with its own programming language, in which numerical algorithms can be implemented.  Several programs use a similar syntax: COMSOL Script, FreeMat, GNU Octave, LabVIEW (in MathScript blocks), O-Matrix, Rlab, Scilab, and Sysquake.
 * MCSim a Monte Carlo simulation tool.
 * NA WorkSheet is a collective aggregation of algorithms coded in Java that implements various Numerical Analysis solutions/techniques in one easy to use opensource tool.
 * NCAR Command Language is an interpreted language designed specifically for scientific data analysis and visualization.
 * numberGo Publisher is a data analysis tool that lets you pivot and chart data, and save it as a portable document.
 * O-Matrix
 * Origin, a software package that is widely used for making scientific graphs. It comes with its own C/C++ compiler that conforms quite closely to ANSI standard.
 * The Ox programming language is a proprietary programming language with a mathematical and statistical function library.
 * Pardiso is a solver for large sparse linear systems on shared memory multiprocessors.
 * PAW is a free data analysis package developed at CERN.
 * Perl Data Language, also known as PDL, an array extension to Perl ver.5, used for data manipulation, statistics, numerical simulation and visualization.
 * Portable, Extensible Toolkit for Scientific Computation (PETSc), is a suite of data structures and routines for the scalable (parallel) solution of scientific applications modeled by partial differential equations.
 * PSPP, an application for statistical analysis.
 * Python programming language:
 * 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
 * SciPy, a library of scientific tools, package includes NumPy
 * ScientificPython, a library with a different set of scientific tools
 * matplotlib, a MATLAB-like plotting library.
 * PyNGL is used to analyze and visualize scientific data, with an emphasis on high quality 2D visualizations.
 * SAGE is a distribution of OS math software, with an unified Python interface which is available as a text interface or a graphical web-based one. Includes interfaces for Open Source and proprietary general purpose CAS, and other numerical analysis programs, like PARI/GP, GAP, gnuplot, Magma, and Maple.
 * R is a widely used system with a focus on data manipulation and statistics which implements the S language. Many add-on packages are available (free software, GNU GPL license).
 * Rlab is another free software program which bears a strong resemblance to MATLAB. Rlab development ceased for several years but it was revived as RlabPlus.
 * ROOT is a free object oriented multipurpose data analysis package, developed at CERN.
 * S-Lang is an (array-based) programming language with strong numerical support.
 * SALOME is a free software that provides a generic platform for pre- and post-processing for numerical simulation.
 * Scilab is similar to MATLAB and Octave. Distributed with source (under their own license, which is not approved by the Open Source Initiative).
 * Shogun, an open source Large Scale Machine Learning toolbox that provides several SVM implementations (like libSVM, SVMlight) under a common framework and interfaces to Octave, Matlab, Python, R
 * Sollya, a tool environment for safe floating-point code development. It is particularly targeted to the automatized implementation of mathematical floating-point libraries.
 * Sysquake is a computing environment with interactive graphics for mathematics, physics and engineering. Like other applications from Calerga, it is based on a MATLAB-compatible language.
 * 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.
 * TK Solver &mdash; Built-in interative solver and extensive library of standard numerical methods.
 * Weka is a suite of machine learning software written at the University of Waikato.
 * XNUMBERS &mdash; Multi Precision Floating Point Computing and Numerical Methods for EXCEL.
 * Yorick is an interpreted programming language designed for numerics, graph plotting and simulation.

CC4 is version 4 of the Calculus Calculator. CC4 includes matrices and infinite precision arithmetic. It is DOS-based but quite an impressive tool. It was developed in the Department of Mathematics at San Francisco State University.