Abstract
In many real-life applications, physical considerations lead to the necessity to consider the smoothest of all signals that is consistent with the measurement results. Usually, the corresponding optimization problem is solved in statistical context. In this paper, we propose a quadratic-time algorithm for smoothing aninterval function. This algorithm, givenn+1 intervals x0, ..., x n with 0 ∈ x0 and 0 ∈ x n , returns the vectorx 0, ...,x n for whichx 0=x 0=0,x i ∈ x i , and Σ(x i+1−x i )2 → min.
Abstract
Во многих практических приложениях из физических соображений требуется найти самую гладкую из всех сигнальных функций, совместимую с даннымн измерений. Как правило, соответствующая задача оптимизации решается статистическим методами. В работе предлагается алгоритм с квадратичным временем выполнения, сглаживающий функцию. Получив на входеn+1 интервалов x0, ..., x n , где 0 ∈ x0 и 0 ∈ x n , алгоритм возвращает векторx 0, ...,x n , для которогоx 0=x n =0,x ni ∈ x i и Σ(x i +1−x i )2 → min.
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V. Kreinovich, K. Villaverde, 1996
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Kreinovich, V., Villaverde, K. A quadratic-time algorithm for smoothing interval functions. Reliable Comput 2, 255–264 (1996). https://doi.org/10.1007/BF02391699
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DOI: https://doi.org/10.1007/BF02391699