Kreinovich, Vladik
Invited Talks
From Interval Computations to ConstraintRelated Set Computations: Towards Faster Estimation of Statistics and ODEs under Interval and pBox Uncertainty (Invited Talk)
Abstract
Interval computations estimate the uncertainty of the result of data processing in situations in which we only know the upper bounds $\Delta$ on the measurement errors. In this case, based on the measurement result $\widetilde x$, we can only conclude that the actual (unknown) value $x$ of the desired quantity is in the interval $[\widetilde x\Delta,\widetilde x+\Delta]$.
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 {\it 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 formalism enables us to find estimates in feasible (polynomial) time.
BibTeX  Entry
@InProceedings{kreinovich:OASIcs:2009:2251,
author = {Vladik Kreinovich},
title = {{From Interval Computations to ConstraintRelated Set Computations: Towards Faster Estimation of Statistics and ODEs under Interval and pBox Uncertainty (Invited Talk)}},
booktitle = {6th International Conference on Computability and Complexity in Analysis (CCA'09)},
series = {OpenAccess Series in Informatics (OASIcs)},
ISBN = {9783939897125},
ISSN = {21906807},
year = {2009},
volume = {11},
editor = {Andrej Bauer and Peter Hertling and KerI Ko},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2009/2251},
URN = {urn:nbn:de:0030drops22516},
doi = {http://dx.doi.org/10.4230/OASIcs.CCA.2009.2251},
annote = {Keywords: Interval computations, set computations, probability boxes, uncertainty, efficient algorithms}
}
2009
Keywords: 

Interval computations, set computations, probability boxes, uncertainty, efficient algorithms 
Seminar: 

6th International Conference on Computability and Complexity in Analysis (CCA'09)

Issue date: 

2009 
Date of publication: 

2009 