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Interval Computations And Interval-Related Statistical Techniques: Estimating Uncertainty Of The Results Of Data Processing And Indirect Measurements, Vladik Kreinovich
Interval Computations And Interval-Related Statistical Techniques: Estimating Uncertainty Of The Results Of Data Processing And Indirect Measurements, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, we only know the upper bound Δ on the measurement error: |Δx| ≤ Δ. In other words, we only know that the measurement error is located on the interval [−Δ, Δ]. The traditional approach is to assume that Δx is uniformly distributed on [−Δ, Δ]. In some situations, however, this approach underestimates the error of indirect measurements. It is therefore desirable to directly process this interval uncertainty. Such "interval computations" methods have been developed since the 1950s. In this paper, we provide a brief overview of related algorithms and results.
Asymptotically Optimal Algorithm For Checking Whether A Given Vector Is A Solution To A Given Interval-Quantifier Linear System, Vladik Kreinovich
Asymptotically Optimal Algorithm For Checking Whether A Given Vector Is A Solution To A Given Interval-Quantifier Linear System, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, we have a linear dependence between different quantities. In such situations, we often need to solve the corresponding systems of linear equations. Often, we know the parameters of these equations with interval uncertainty. In this case, depending on the practical problem, we have different notions of a solution. For example, if we determine parameters from observations, we are interested in all the unknowns which satisfy the given system of linear equations for some possible values of the parameters. If we design a system so that it does not exceed given tolerance bounds, then we need to …