Abstract
We consider the problem of approximation of continuous functions by generalized polynomials in the case where the values of the function at the observation points are known with random errors. We construct confidence limits with a given significance level for the true values of the function at any point of its domain of definition.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. G. Krein, Yu. I. Petunin, and E. M. Semenov, Interpolation of Linear Operators [in Russian], Nauka, Moscow (1978).
N. V. Smirnov and I. V. Dunin-Barkovskii, A Course in Probability Theory and Mathematical Statistics [in Russian], Nauka, Moscow (1965).
G. M. Fikhtengol’ts, A Course in Differential and Integral Calculus [in Russian], Vol. 2, Nauka, Moscow (1961).
N. P. Korneichuk, Splines in the Theory of Approximation [in Russian], Nauka, Moscow (1984).
Yu. S. Zav’yalov, B. I. Kvasov, and V. L. Miroshnichenko, Methods of Spline Functions [in Russian], Nauka, Moscow (1980).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 9, pp. 1244–1249, September, 1998.
Rights and permissions
About this article
Cite this article
Savkina, M.Y. Approximation of continuous functions with random errors in observed values. Ukr Math J 50, 1424–1430 (1998). https://doi.org/10.1007/BF02525248
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02525248