Kreinovich, Vladik; Villaverde, Karen A quadratic-time algorithm for smoothing interval functions. (English) Zbl 0858.65011 Reliab. Comput. 2, No. 3, 255-264 (1996). 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 Keywords:smoothing interval functions; quadratic-time algorithm PDFBibTeX XMLCite \textit{V. Kreinovich} and \textit{K. Villaverde}, Reliab. Comput. 2, No. 3, 255--264 (1996; Zbl 0858.65011) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.