Introduction to Interval Arithmetic and to some Interval-Based Software Systems and Libraries
N. Revol (INRIA, France)
The main principles and advantages of interval arithmetic will be discussed.
Some libraries that implement interval arithmetic will then be presented and compared. Differences in the adopted definitions will be emphasized, mainly in dealing with infinities and division by an interval containing 0. Among such libraries one can quote C-XSC and filib, Boost C++, Profil-BIAS, COSY for Taylor models, and MPFI.
Finally, some solvers based on interval arithmetic will be introduced:
- solvers for nonlinear systems (such as SIVIA, Alias or CLP and RealPaver based on constraint propagation);
- solvers for global optimization (e.g. GlobSol);
- solvers for linear algebra (e.g. IntLab);
- solvers for ODEs (such as ValEncIA-IVP, VNODE, VSPODE).