Abstract
In a Hilbert space with Gaussian measure, we obtain an estimate for the accuracy of interpolation of an entire operator in the case where its values are perturbed at nodes and determine the value of the degree of an interpolation polynomial the exceeding of which does not improve the estimate of the accuracy of interpolation.
Similar content being viewed by others
REFERENCES
A. D. Egorov, P. N. Sobolevskii, and L. A. Yanovich, Approximate Methods of Calculation of Continual Integrals [in Russian], Nauka i Tekhnika, Minsk (1985).
P. M. Prenter, “Lagrange and Hermite interpolation in Banach spaces,” Approxim. Theory, 4, No. 4, 419–432 (1971).
V. L. Makarov, V. V. Khlobystov, and L. A. Yanovich, Interpolation of Operators [in Russian], Naukova Dumka, Kiev (2000).
W. A. Porter, “Synthesis of polynomic system,” SIAM J. Math. Anal., 11, No. 2, 308–315 (1980).
K. I. Pupkov, V. I. Kapalin, and A. S. Yushchenko, Functional Series in the Theory of Nonlinear Systems [in Russian], Nauka, Moscow (1976).
W. A. Porter, “Data interpolation, causality structure and system identification,” Inform. Contr., No. 29, 217–233 (1975).
V. L. Makarov and V. V. Khlobystov, Foundations of the Theory of Polynomial Operator Interpolation [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1998).
V. V. Khlobystov, “On the problem of convergence of interpolation processes in a Hilbert space,” Kiber. Sist. Analiz, No. 6, 166–172 (2000).
V. V. Khlobystov and E. F. Kashpur, “On the problem of interpolation of polynomial operators,” Kiber. Sist. Analiz, No. 3, 102–108 (1996).
V. V. Khlobystov and E. F. Kashpur, “On the accuracy of the polynomial interpolation in a Hilbert space in the case of perturbed values of the operator at nodes,” Kiber. Sist. Analiz, No. 1, 168–173 (2002).
I. I. Gikhman and A. V. Skorokhod, Theory of Random Processes [in Russian], Vol. 1, Nauka, Moscow (1971).
V. Khlobystov and E. Kashpur, “On the convergence of an interpolation process with minimal norm in a Hilbert space,” Zh. Obchysl. Prykl. Mat., 84, No. 1, 124–127 (1999).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Khlobystov, V.V., Kashpur, E.F. Analysis of the Accuracy of Interpolation of Entire Operators in a Hilbert Space in the Case of Perturbed Nodal Values. Ukrainian Mathematical Journal 55, 1153–1162 (2003). https://doi.org/10.1023/B:UKMA.0000010612.26370.80
Issue Date:
DOI: https://doi.org/10.1023/B:UKMA.0000010612.26370.80