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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. 145-156, 2023/09/13
Padé-type approximants are rational functions that approximate a given formal power series. Boutry [Numer. Algorithms, 33 (2003), pp 113–122] constructed Padé-type approximants that correspond to the averaged Gauss quadrature rules introduced by Laurie [Math. Comp., 65 (1996), pp. 739–747]. More recently, Spalević [Math. Comp., 76 (2007), pp. 1483–1492] proposed optimal averaged Gauss quadrature rules, that have higher degree of precision than the corresponding averaged Gauss rules, with the same number of nodes. This paper defines Padé-type approximants associated with optimal averaged Gauss rules. Numerical examples illustrate their performance.
Keywords: Gauss quadrature, averaged Gauss quadrature, optimal averaged Gauss quadrature, Padé-type approximant