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Full-Text Articles in Physical Sciences and Mathematics
What If We Use Almost-Linear Functions Instead Of Linear Ones As A First Approximation In Interval Computations, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich
What If We Use Almost-Linear Functions Instead Of Linear Ones As A First Approximation In Interval Computations, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, the only information that we have about measurement errors is the upper bound on their absolute values. In such situations, the only information that we have after the measurement about the actual (unknown) value of the corresponding quantity is that this value belongs to the corresponding interval: e.g., if the measurement result is 1.0, and the upper bound is 0.1, then this interval is [1.0−0.1,1.0+0.1] = [0.9,1.1]. An important practical question is what is the resulting interval uncertainty of indirect measurements, i.e., in other words, how interval uncertainty propagates through data processing. There exist feasible algorithms …
Global Independence, Possible Local Dependence: Towards More Realistic Error Estimates For Indirect Measurements, Vladik Kreinovich
Global Independence, Possible Local Dependence: Towards More Realistic Error Estimates For Indirect Measurements, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, it is not realistically possible to directly measure the desired physical quantity. In such situations, we have to measure this quantity indirectly, i.e., measure related quantities and use the known relation to estimate the value of the desired quantity. How accurate it the resulting estimate? The traditional approach assumes that the measurement errors of all direct measurements are independent. In many practical situations, this assumption works well, but in many other practical situations, it leads to a drastic underestimation of the resulting estimation error: e.g., when we base our estimate on measurements performed at nearby moments …
When Can We Simplify Data Processing: An Algorithmic Answer, Julio Urenda, Olga Kosheleva, Vladik Kreinovich, Berlin Wu
When Can We Simplify Data Processing: An Algorithmic Answer, Julio Urenda, Olga Kosheleva, Vladik Kreinovich, Berlin Wu
Departmental Technical Reports (CS)
In many real-life situations, we are interested in the values of physical quantities x1, ..., xn which are difficult (or even impossible) to measure directly. To estimate these values, we measure easier-to-measure quantities y1, ..., ym which are related to the desired quantities by a known relation, and use these measurement results to estimate xi. The corresponding data processing algorithms are sometimes very complex and time-consuming, so a natural question is: are simpler (and, thus, faster) algorithms possible for solving this data processing problem? In this paper, we show that by using …