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A quadratic-time algorithm for smoothing interval functions. (English) Zbl 0858.65011

The authors consider the following problem: given \(n-1\) intervals \(X_1, \dots, X_{n-1}\), find \(n-1\) numbers \(x_i\), \(i=1,\dots,n-1\), such that \(x_i\) belongs to \(X_i\) for \(i=1, \dots, n-1\) and the sum of the squares of the differences \(x_i-x_{i-1}\), \(i=1, \dots, n\), is minimal \((x_0 = x_n=0)\). A quadratic-time algorithm for the solution of this problem is proposed.
Reviewer: S.Markov (Sofia)

MSC:

65D10 Numerical smoothing, curve fitting
65G30 Interval and finite arithmetic
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References:

[1] Cormen, Th. H., Leiserson, C. E., and Rivest, R. L.Introduction to algorithms. MIT Press, Cambridge, MA, and Mc-Graw Hill Co., N.Y., 1990. · Zbl 1158.68538
[2] Glasko, V. B.Inverse problems of mathematical physics. American Institute of Physics, N.Y., 1984. · Zbl 0542.35002
[3] Inverse problems. SIAM-AMS Proceedings 14, American Mathematical Society, Providence, RI, 1983.
[4] Inverse problems. Birkhauser Verlag, Basel, 1986. · Zbl 0646.73013
[5] Inverse problems. Lecture Notes in Mathematics1225, Springer-Verlag, Berlin-Heidelberg, 1986.
[6] Jájá, J.An introduction to parallel algorithms. Addison-Wesley, Reading, MA, 1992. · Zbl 0781.68009
[7] Kreinovich, V., Quintana, C., Lea, R., Fuentes, O., Lokshin, A., Kumar, S., Boricheva, I., and Reznik, L.What non-linearity to choose? Mathematical foundations of fuzzy control. In: ”Proceedings of the 1992 International Conference on Fuzzy Systems and Intelligent Control”, Louisville, KY, 1992, pp. 349–412.
[8] Lavrentiev, M. M., Romanov, V. G., and Shishatskii, S. P.Ill-posed problems of mathematical physics and analysis. American Mathematical Society, Providence, RI, 1986.
[9] Tikhonov, A. N. and Arsenin, V. Y.Solutions of ill-posed problems. V. H. Winston & Sons, Washington, DC, 1977. · Zbl 0354.65028
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