IJPAM: Volume 76, No. 1 (2012)

ESTIMATES OF DIVIDED DIFFERENCES
OF REAL-VALUED FUNCTIONS DEFINED WITH A NOISE

Sergei P. Sidorov$^1$, Vladimir Balash$^2$
$^1$Department of Mechanics and Mathematics
Saratov State University
83, Astrakhanskaya, Saratov 410012, RUSSIAN FEDERATION
$^2$School of Information Systems, Computing and Mathematics
Brunel University
London, UNITED KINGDOM


Abstract. Suppose that point evaluations of a real-valued function $f$ at points $x_{0 },\ldots, x_{k}$ 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 $k$-th divided difference of the function $f$. 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
Year: 2012
Volume: 76
Issue: 1