Volume 59, pp. 145-156, 2023.

Optimal averaged Padé-type approximants

Dusan Lj. Djukić, Rada M. Mutavdžić Djukić, Lothar Reichel, and Miodrag M. Spalević

Abstract

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.

Full Text (PDF) [299 KB], BibTeX

Key words

Gauss quadrature, averaged Gauss quadrature, optimal averaged Gauss quadrature, Padé-type approximant

AMS subject classifications

65D30, 65D32

Links to the cited ETNA articles

[16]	Vol. 45 (2016), pp. 371-404 Sotirios E. Notaris: Gauss-Kronrod quadrature formulae - A survey of fifty years of research
[18]	Vol. 50 (2018), pp. 1-19 Stefano Pozza, Miroslav S. Pranić, and Zdeněk Strakoš: The Lanczos algorithm and complex Gauss quadrature

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