Internality of generalized averaged Gauss quadrature rules and truncated variants for modified Chebyshev measures of the third and fourth kinds

Djukić, Dušan Lj.; Djukić, Rada M. Mutavdžić; Reichel, Lothar; Spalević, Miodrag M.

doi:10.1007/s11075-022-01385-w

Numer Algor

2022

DOI: 10.1007/s11075-022-01385-w

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Internality of generalized averaged Gauss quadrature rules and truncated variants for modified Chebyshev measures of the third and fourth kinds

Dušan Lj. Djukić

Rada M. Mutavdžić Djukić

Lothar Reichel

et al.

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Cited by 4 publications

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“…Spalević [22] derived a new representation of these rules and introduced optimal averaged rules for more general nonnegative real measures. For properties and applications of optimal averaged Gauss rules associated with nonnegative real measures; see [6,7,15,20,23] and references therein.…”

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confidence: 99%

Optimal averaged Padé-type approximants

Djukić,

Mutavdžić Djukić,

Reichel

et al. 2023

etna

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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.

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Optimal averaged Padé-type approximants

Djukić,

Mutavdžić Djukić,

Reichel

et al. 2023

etna

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Weighted averaged Gaussian quadrature rules for modified Chebyshev measures

Djukić

Reichel

et al. 2024

Applied Numerical Mathematics

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A new class of quadrature rules for estimating the error in Gauss quadrature

Pejčev,

Reichel,

Spalević

et al. 2024

Applied Numerical Mathematics

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Internality of generalized averaged Gauss quadrature rules and truncated variants for modified Chebyshev measures of the third and fourth kinds

Cited by 4 publications

References 21 publications

Optimal averaged Padé-type approximants

Optimal averaged Padé-type approximants

Weighted averaged Gaussian quadrature rules for modified Chebyshev measures

A new class of quadrature rules for estimating the error in Gauss quadrature

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