Interval and Related Software
Interval and Verified Software
a C-XSC library for the verified
automatic computation of estimates for Taylor
coefficients of analytic functions.
- AERN, Approximating Exact Real Numbers,
a Haskell library for rigorous and exact real number and real function computation
Library, Algorithms Library of Interval Analysis for Systems; see
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.
a package for verified reachability analysis of hybrid systems that
includes a library for verified set-based computation
a software package for verified solution of ordinary
Global Optimization Software.
Purely continuous, purely integer, and
mixed-integer nonlinear problems can be solved with the
interval C++ library
implemented within the popular BOOST project
- CAPD, Computer-Assisted Proofs in Dynamics (also available at
package for rigorous numerics for dynamical systems, oriented mostly
for computer assisted proofs in dynamics.
This library provides 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
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
Among other applications, it allows rigorous modeling of hybrid systems
CLP(BNR), a Constraint Interval-Arithmetic
This package is actually
a language for Constraint Logic Programming based on
a library of complex interval standard functions.
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
MIT-produced symbolic and numeric library for general numerical
calculations which uses interval computations.
an automatic differentiation package, with applications to verified
solution of ordinary differential equations.
Fast Interval LIRrary, a C++ library on extended interval arithmetic.
- Interval arithmetic library for
a special programming language Frink (implemented in Java)
Interval Arithmetic package for
manipulating finite sets of (possibly unbounded) intervals; there is
- software for global solutions; downloading instructions
This package allows analysis of hybrid systems with
non-linear ODEs over an unbounded time horizon, uses intervals as its main
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
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.
Interval COnstraints Solver
libraries for interval computations and constraint satisfaction.
- INTBLAS: C++
An implementation of
INTerval Basic Linear Algebra Software.
arithmetic for ADA
arithmetic in Sun's Forte C++ compiler
arithmetic in Sun's Forte Fortran 95 compiler
- Interval library is a part of Intel
Math Kernel Library (MKL).
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
Software in Fortran-77
Interval Software in Fortran-90
This Fortran-90 module is actually a
language for interval computations
- Interval based Java applets:
and Wuppertal interval software
- Libaffa; a
C++ affine arithmetic library for GNU/Linux
- Maple: Interval Software in Maple and its clones:
- Mathematica based
supports dynamic interval web computations and visualization.
- Matlab: Interval Software in Matlab:
- 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
- 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.
Multiple Precision Floating-Point Interval Library
integrates interval computation in its kernel;
both Maple and MuPad are integrated into Scientific Workplace
- GNU Octave
The package conforms to IEEE Interval
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
A fast C++ library for interval
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.
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.
solves quantified inequality
A library of C routines for interval
arithmetic and constraint narrowing
interval and constraint propagation library smathlib
and a functional programming language
Software for interval-based arithmetic on
a free C++ geometric
modeller that is substantially based on interval arithmetic
A solver based on interval constraint propagation. It
allows to tackle nonlinear algebraic systems with real
and/or integer variables.
software for VALidation of state ENClosures using
Interval Arithmetic for Initial Value Problems
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)
languages and fi_lib
CBDO: A Matlab toolbox for Cloud Based Design Optimization
Software for uncertainty modeling by clouds,
by Martin Fuchs
Control of Accuracy and Debugging for Numerical Appplications
Software for estimating propagation of
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
Software that extends operations with intervals
to operations with probability distributions.
A free app for iPhone/iPod/iPad, performs
real root isolation
and a few other polynomial functions.
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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