Abstract
When we have only interval ranges [xi, xi] of sample values x1,…, xn, what is the interval [V, V] of possible values for the variance V of these values? We prove that the problem of computing the upper bound V is NP-hard. We provide a feasible (quadratic time) algorithm for computing the lower bound V on the variance of interval data. We also provide a feasible algorithm that computes V under reasonable easily verifiable conditions.
- V. Kreinovich, A. Lakeyev, J. Rohn, and P. Kahl, Computational complexity and feasibility of data processing and interval computations, Kluwer, Dordrecht, 1997.Google Scholar
- R. Osegueda, V. Kreinovich, L. Potluri, and R. Aló, "Non-Destructive Testing of Aerospace Structures: Granularity and Data Mining Approach", Proceedings of FUZZ-IEEE'2002, Honolulu, Hawaii, May 12-17, 2002 (to appear).Google ScholarCross Ref
- S. A. Vavasis, Nonlinear optimization: complexity issues, Oxford University Press, N.Y., 1991. Google ScholarDigital Library
- G. W. Walster, "Philosophy and practicalities of interval arithmetic", In: R. E. Moore (ed.), Reliability in Computing, 1988, pp. 307-323. Google ScholarDigital Library
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