Michel Goze

Nicolas Goze, Michel Goze, Abdel Kenoufi et al.

In this paper we propose some very promissing results in interval arithmetics which permit to build well-defined arithmetics including distributivity of multiplication and division according addition and substraction. Thus, it allows to build all algebraic operations and functions on intervals. This will avoid completely the wrapping effects and data dependance. Some simple applications for matrix eigenvalues calculations, inversion of symmetric matrices and finally optimization are exhibited in the object-oriented programming language python.

Abdelouahab Kenoufi, Nicolas Goze, Michel Goze

In this paper, we present how to use a free algebra based interval arithmetics framework in order to build better defined inclusion function for interval semi-group and for its associated vector space. One introduces the psi-algorithm, which performs set inversion of functions and exhibits some numerical examples developped with the python programming langage.