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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. 582-596, 2023/11/30
The problem of recovering the mixed derivative $f^{(2,2)}$ for bivariate functions is investigated.Based on the truncation method, a numerical differentiation algorithm is constructedthat uses perturbed Fourier–Legendre coefficients of the function as input information.Moreover, the ideaof a hyperbolic crossis implemented,which makes it possible to significantly reduce computational costs.It is established that this algorithm guarantees order-optimal accuracy (in the power scale) witha minimal amount of Galerkin information involved.
Keywords: numerical differentiation, Legendre polynomials, truncation method, information complexity, optimal error estimates