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ETNA - Electronic Transactions on Numerical Analysis
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |
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DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
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ETNA - Electronic Transactions on Numerical Analysis, pp. 320-341, 2020/06/25
As it is known, the convergence rate of the multidimensional Whittaker-Kotelnikov-Shannon (WKS) sampling series is slow due to the slow decay of the sinc function. In this paper, we incorporate a convergence factor from the Bernstein space into the multidimensional WKS sampling series to establish regularized sampling and a corresponding improved convergence rate. The convergence rate of this regularized series depends on the decay of the convergence factor. Various bounds for the truncation of the regularized sampling series are investigated depending on the convergence factor. Furthermore, we estimate two types of perturbation errors associated with this series. Some numerical experiments are presented.
Keywords: multidimensional sampling, error analysis, convergence rate