When we have n results x 1,...,x n of repeated measurement of the same quantity, the traditional statistical approach usually starts with computing their sample average E and their sample variance V. Often, due to the inevitable measurement uncertainty, we do not know the exact values of the quantities, we only know the intervals x i of possible values of x 1 In such situations, for different possible values x i∈ x i, we get different values of the variance. We must therefore find the range V of possible values of V. It is known that in general, this problem is NP-hard. For the case when the measurements are sufficiently accurate (in some precise sense), it is known that we can compute the interval V in quadratic time O(n2). In this paper, we describe a new algorithm for computing V that requires time O(n log(n)) (which is much faster than O(n 2)).
Reliable Computing – Springer Journals
Published: Jan 1, 2006
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