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The use of multi-intervals in the UniCalc solver. (English) Zbl 0848.65041

Alefeld, Götz (ed.) et al., Scientific computing and validated numerics. Proceedings of the international symposium on scientific computing, computer arithmetic and validated numerics SCAN-95, Wuppertal, Germany, September 26-29, 1995. Berlin: Akademie Verlag. Math. Res. 90, 91-97 (1996).
In the context of research on knowledge representation and processing in the Novosibirsk division of the Russian Research Institute of Artificial Intelligence, the method of so-called subdefinite computations was proposed. This method can be regarded as an analog of constraint propagation with interval labels, although we believe that it is broader, since it enables one to treat simultaneously continuous and discrete domains, allows other representations of imprecise objects besides intervals, and can be extended with new “subdefinite” objects, such as subdefinite functions and subdefinite relations. With the use of the apparatus of subdefinite computations, various types of subdefinite data (integers and reals, sets, logical and enumerable data, objects of planimetry, etc.) were implemented, and several application systems were built in the Institute. An example of such systems is UniCalc, a solver of systems of algebraic equations.
The implementation of the subdefinite calculation algorithm (SCA) uses an interval representation of subdefinite values, which often necessitates the result to include domains certainly free from solutions (details to follow). In the present work we consider a multi-interval representation of subdefinite values which allows to avoid this disadvantage and to expand the abilities of the solver. The representation allows not only to restrict the range of possible values but to exclude the domains which certainly do not contain solutions.
For the entire collection see [Zbl 0836.00039].

MSC:

65H10 Numerical computation of solutions to systems of equations
65G30 Interval and finite arithmetic
68T30 Knowledge representation

Software:

UniCalc
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