IJPAM: Volume 76, No. 1 (2012)
OF REAL-VALUED FUNCTIONS DEFINED WITH A NOISE
Department of Mechanics and Mathematics
Saratov State University
83, Astrakhanskaya, Saratov 410012, RUSSIAN FEDERATION
School of Information Systems, Computing and Mathematics
London, UNITED KINGDOM
Abstract. Suppose that point evaluations of a real-valued function at points are known with a noise error that continuously uniformly distributed on [-1,1]. In this paper we find the lower bound of the "worst"-case error (as well as the mean error) of absolute value of -th divided difference of the function . The case of the Gaussian-type error of point evaluations of functions is examined as well.
Received: November 15, 2011
AMS Subject Classification: 65D05, 65D25
Key Words and Phrases: fuzzy interpolation, divided difference, fuzzy approximation
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395