• ADHC, Algorithmic Differentiation and Hull-Consistency-enforcing C++ template library; see also this link
• AERN, Approximating Exact Real Numbers, a Haskell library for rigorous and exact real number and real function computation
• 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
• 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
• CAPD, Computer-Assisted Proofs in Dynamics (also available at this website), a C++ package for rigorous numerics for dynamical systems, oriented mostly for computer assisted proofs in dynamics; this library provides rigorous solvers for ODEs, variational equations for ODEs, differential inclusions, automatic computation of Poincare maps and their derivatives, computation of homology of spaces, maps and many other features
• CGAL, Computational Geometry Algorithms Library, written in C++, uses interval computations to make geometric computations robust and efficient
• CLIP; among other applications, it allows rigorous modeling of hybrid systems
• 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
• C-XCS Software
• filib++, Fast Interval LIRrary, a C++ library on extended interval arithmetic; see also this site
• General Interval Arithmetic package for manipulating finite sets of (possibly unbounded) intervals; there is an applet interface
• GlobSol - software for global solutions; downloading instructions
• GNU Octave interval package; the package conforms to IEEE Interval Standard 1788
• HIBA_USNE, Heuristical Interval Branch-and-bound ALgorithm for solving Underdetermined and well-determined Systems of Nonlinear Equations; see also this link
• 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 Matlab
• ICOS, Interval COnstraints Solver
• InC++ libraries for interval computations and constraint satisfaction.
• 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 arithmetic library for a special programming language Frink (implemented in Java)
• INTLAB - INTerval LABoratory, an interval toolbox for Matlab
• intpakX combines interval arithmetic with the features of a Computer Algebra System
• Karlsruhe and Wuppertal interval software
• kv, a C++ Library for Verified Numerical Computation
• Libaffa; a C++ affine arithmetic library for GNU/Linux
• Maple is integrated into Scientific Workplace
• Mathematica based web site supports dynamic interval web computations and visualization.
• 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
• 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.
• 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
• survive-CXSC,, a fork of the C-XSC library
• VALENCIA-IVP, software for VALidation of state ENClosures using Interval Arithmetic for Initial Value Problems
• VERSOFT, Verified software in Matlab and Intlab: Files for solving various linear and quadratic problems with interval or real data
• VNODE-LP, a C++ based Interval Solver for Initial Value Problems in Ordinary Differential Equations
• VSDP (Verified SemiDefinite Programming), a MATLAB software package for computing verified (rigorous) results for semidefinite programming problems
• XSC languages (C-XSC, PASCAL-XSC), Scientific Computing with Validation, Arithmetic Requirements, Hardware Solution and Language Support; see also this link and this link
• XSC software

• 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.

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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