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- W40418771 abstract "One of the main problems of interval computations is to find an enclosure Y ⊇ f(X1, . . . , Xn) for a range of a given function f(x1, . . . , xn) over given intervals X1, . . . , Xn. Most of the techniques for estimating this range are based on propagating the range through computations. Specifically, we follow the computations of f(x1, . . . , xn) step-by-step: we start with ranges X1, . . . , Xn of the inputs, and then we sequentially compute the enclosures for the ranges of all intermediate results, until, on the last computation step, we get the desired enclosure Y . A similar propagation of “decorations” – information about continuity – enables us to make conclusions about the continuity of the resulting function f(x1, . . . , xn). In this paper, we show that the interval propagation results can be naturally extended to the general case of arbitrary sets. For this general case, we provide necessary and sufficient conditions for such a propagation. 1 Computations: From Real Values to General Sets How to describe quantities. Usually, the values of physical quantities are described by real numbers. However, some physical quantities require a more complex description : e.g., some quantities are characterized by a vector (e.g., force or velocity), some by a function (e.g., a current value of a field) or by a geometric shape. In view of this possibility, we will assume that the set S of possible values of each quantity is not necessarily a set of real numbers, it can be a general set." @default.
- W40418771 created "2016-06-24" @default.
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- W40418771 date "2011-01-01" @default.
- W40418771 modified "2023-09-27" @default.
- W40418771 title "Propagating Range (Uncertainty) and Continuity Information Through Computations: From Real-Valued Intervals to General Sets" @default.
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