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CCA
2009
Springer

From Interval Computations to Constraint-Related Set Computations: Towards Faster Estimation of Statistics and ODEs under Interv

8 years 12 months ago
From Interval Computations to Constraint-Related Set Computations: Towards Faster Estimation of Statistics and ODEs under Interv
Interval computations estimate the uncertainty of the result of data processing in situations in which we only know the upper bounds ∆ on the measurement errors. In this case, based on the measurement result x, we can only conclude that the actual (unknown) value x of the desired quantity is in the interval [x − ∆, x + ∆]. In interval computations, at each intermediate stage of the computation, we have intervals of possible values of the corresponding quantities. As a result, we often have bounds with excess width. To remedy this problem, in our previous papers, we proposed an extension of interval technique to set computations, where on each stage, in addition to intervals of possible values of the quantities, we also keep sets of possible values of pairs (triples, etc.). In this paper, we show that in several practical problems, such as estimating statistics (variance, correlation, etc.) and solutions to ordinary differential equations (ODEs) with given accuracy, this new fo...
Vladik Kreinovich
Added 24 Jul 2010
Updated 24 Jul 2010
Type Conference
Year 2009
Where CCA
Authors Vladik Kreinovich
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