• ACETAF, a C-XSC library for the verified automatic computation of estimates for Taylor coefficients of analytic functions.
• AERN, distributed arbitrary precision packages for verifiably Approximating Exact Real Numbers
• ALIAS Library, Algorithms Library of Interval Analysis for Systems; see also this link
• AQCS, a free software package for Approximate Quantified Constraint Solving - computes box approximations of the solution set of formulae of the first-order predicate language over the reals.
• Ariadne, a package for verified reachability analysis of hybrid systems that includes a library for verified set-based computation
• AWA, a software package for verified solution of ordinary differential equations.
• BARON, Global Optimization Software.
  Purely continuous, purely integer, and mixed-integer nonlinear problems can be solved with the software.
• BOOST interval C++ library implemented within the popular BOOST project
• CGAL, Computational Geometry Algorithms Library, written in C++, uses interval computations to make geometric computations robust and efficient; the related part of CGAL manual can be found at the following site the CLIP
• CLIP
  Among other applications, it allows rigorous modeling of hybrid systems
• CLP(BNR), a Constraint Interval-Arithmetic Package
  This package is actually a language for Constraint Logic Programming based on Interval Arithmetic.
• CoStLy, a library of complex interval standard functions.
• COSY. This software package is based on Taylor model and interval methods. It is intended for verified solution of such problems as ordinary differential equations, quadrature, range bounding, etc. It can either be used as a stand-alone program or via C++ and Fortran 90/95 frontends.
• DAEPACK, MIT-produced symbolic and numeric library for general numerical calculations which uses interval computations.
• FADBAD/TADIFF, an automatic differentiation package, with applications to verified solution of ordinary differential equations.
• filib++, Fast Interval LIRrary, a C++ library on extended interval arithmetic.
• Interval arithmetic library for a special programming language Frink (implemented in Java)
• General Interval Arithmetic package for manipulating finite sets of (possibly unbounded) intervals; there is an applet interface
• GlobSol - software for global solutions; downloading instructions
• HSolver
  This package allows analysis of hybrid systems with non-linear ODEs over an unbounded time horizon, uses intervals as its main work-horse
• HySAT, A bounded model checker for hybrid systems
  The package allows bounded-time analysis of hybrid systems with complex discrete structure, also uses intervals for reasoning about numerical constraints
• ICE, Interval Calculator for Engineers
  Intervals are to be entered like min_max or mean%tol, for example: 1_2, 4_3, 4%2. The help section of this ICE is full of examples and explanations to use properly the syntax which looks like Mathlab.
• ICOS, Interval COnstraints Solver
• InC++ libraries for interval computations and constraint satisfaction.
• INTBLAS: C++ Implementation
  An implementation of INTerval Basic Linear Algebra Software.
• Interval arithmetic for ADA
  This library serves as a basis for a Fuzzy Computations Package
• Interval arithmetic in Sun's Forte C++ compiler
• Interval arithmetic in Sun's Forte Fortran 95 compiler
• Interval library is a part of Intel Math Kernel Library (MKL).
  It includes interval arithmetic (standard and two complex) and interval linear solvers that compute enclosures (sharp or fast) of the solution set to interval linear systems of equations, check properties of interval matrices; some part of the solvers works with complex intervals. Questions and suggestions are welcome at MKL forum
• Interval Software in Fortran-77
  
• Interval Software in Fortran-90
  
  This Fortran-90 module is actually a language for interval computations
• Interval based Java applets:
  • Rigorous Gradient Calculator
    Computes the gradient of a function using rigorous interval arithmetic
  • Rigorous Graphing Applet
    Graph functions and finds their roots. All results are verified, no second guess necessary.
  • Cascade Applet
    Rigorously solves the initial value problem for discrete, planar maps. A powerful new algorithm produces guaranteed error bounds in form of zonotope enclosures.
• Karlsruhe and Wuppertal interval software
• Libaffa; a C++ affine arithmetic library for GNU/Linux
• Maple: Interval Software in Maple and its clones:
  • A general webpage with links to Interval Software in Maple
  • Interval Arithmetic PowerTool
  • intpakX combines interval arithmetic with the features of a Computer Algebra System
  • Maple is integrated into Scientific Workplace
• Mathematica based web site supports dynamic interval web computations and visualization.
• Matlab: Interval Software in Matlab:
  • INTLAB - INTerval LABoratory, an interval toolbox for Matlab; free for non-commercial use.
  • VSDP (Verified SemiDefinite Programming),
    a MATLAB software package for computing verified (rigorous) results for semidefinite programming problems.
  • Verified software in Matlab and Intlab
    Files for solving various linear and quadratic problems with interval or real data.
  • Matlab-based b4m, a Matlab toolbox based on BIAS (C++); free for non-commercial use.
  • Acsysteme's Interval Toolbox for Matlab.
    The toolbox provides high level routines for solving low dimensional global optimization problems (with or without constraints) and for solving non-linear systems of equations and inequalities ia set inversion.
• MISO, a software package containing a set of solvers based on Modal Interval Analysis. These solvers are:
  • FSTAR solver: Allows doing computations with Modal Intervals.
  • QRCS solver: Allows proving the satisfiability of a class of quantified real constraints.
  • QSI solver: Allows obtaining inner and outer approximations of the solution set of a class of quantified real constrains.
  • MINIMAX solver: Allows solving constrained minimax optimization problems.
  • SQUALTRACK solver: Allows detecting faults in dynamic systems.
• MPFI, Multiple Precision Floating-Point Interval Library
• MuPAD, integrates interval computation in its kernel; both Maple and MuPad are integrated into Scientific Workplace
• ParaGlobSol
  Parallel/distributed implementations of the interval global optimization FORTRAN 90 package GlobSol, which solves global optimization problems with the interval branch-and-bound algorithm together with interval Newton/generalized bisection method.
• ParLinSys, software for solving parametric interval linear systems
• PROFIL/BIAS
  A fast C++ library for interval arithmetic. Speed and comparisons can be found in:
  O. Knueppel: PROFIL/BIAS - A Fast Interval Library, COMPUTING, Vol. 53, No. 3-4, p. 277-287.
• Pytaylor, a Python package implementing Taylor models and associated guaranteed ODE solvers.
  Pytaylor uses mpmath for interval arithmetic and sympy for symbolic manipulation.
• RealPaver
  Interval software implementing constraint satisfaction techniques for solving nonlinear systems.
• Range software of Oliver Aberth
  A suite of demonstration programs, using variable precision interval arithmetic, that can solve the typical problems of elementary numerical analysis to desired accuracy.
• SMMS
  Software for managing interval systems of equations, developed by Fernando L. Alvarado
• Rsolver
  solves quantified inequality constraints
• smathlib
  A library of C routines for interval arithmetic and constraint narrowing
• Interface between the interval and constraint propagation library smathlib and a functional programming language Objective Caml
• Statool
  Software for interval-based arithmetic on random variables.
• SvLis
  a free C++ geometric modeller that is substantially based on interval arithmetic
• UniCalc
  A solver based on interval constraint propagation. It allows to tackle nonlinear algebraic systems with real and/or integer variables.
• VALENCIA-IVP
  software for VALidation of state ENClosures using Interval Arithmetic for Initial Value Problems
• VNODE-LP
  A C++ based Interval Solver for Initial Value Problems in Ordinary Differential Equations
• XSC software (for more detailed information about XSC languages, see the following page)
  XSC languages and fi_lib

CBDO: A Matlab toolbox for Cloud Based Design Optimization
Software for uncertainty modeling by clouds, by Martin Fuchs
• CADNA, Control of Accuracy and Debugging for Numerical Appplications
  Software for estimating propagation of round-off errors.
• DALSolution,
  Innovative software for the analysis of questionnaire surveys, public polls, medical records, etc.; uses interval-valued probabilities and other interval-related types of partial information about probabilities.
• PDV,
  Software that extends operations with intervals to operations with probability distributions.
• RealRoots,
  A free app for iPhone/iPod/iPad, performs real root isolation and a few other polynomial functions.
• RiskCalc,
  Software for Risk Assessment with Uncertain Numbers, including operations with interval, probabilitistic, and fuzzy uncertainties, and their combination.

See also Languages for Interval Analysis.

See also MathTools.net, a free portal covering computing tools for science and engineering. This portal contains over 20,000 useful links, covering software in Matlab, Java, Excel, C/C+, Fortran, etc.

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