On the Gauss-Kronrod quadrature formula for a modified weight function of Chebyshev type

In this paper, we consider the Gauss-Kronrod quadrature formulas for a modified Chebyshev weight. Efficient estimates of the error of these Gauss–Kronrod formulae for analytic functions are obtained, using techniques of contour integration that were introduced by Gautschi and Varga (cf. Gautschi and...

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Published inNumerical algorithms Vol. 91; no. 4; pp. 1855 - 1877
Main Authors Orive, Ramón, Pejčev, Aleksandar V., Spalević, Miodrag M., Mihić, Ljubica
Format Journal Article
LanguageEnglish
Published New York Springer US 01.12.2022
Springer Nature B.V
Subjects
Algebra
Algorithms
Analytic functions
Chebyshev approximation
Computer Science
Estimates
Numeric Computing
Numerical Analysis
Original Paper
Polynomials
Quadratures
Theory of Computation
Weighting functions
Gauss-Kronrod quadrature formulae
Remainder term for analytic functions
Chebyshev weight function
Primary 65D32
Contour integral representation
Error bound
65D30; Secondary 41A55
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Summary:In this paper, we consider the Gauss-Kronrod quadrature formulas for a modified Chebyshev weight. Efficient estimates of the error of these Gauss–Kronrod formulae for analytic functions are obtained, using techniques of contour integration that were introduced by Gautschi and Varga (cf. Gautschi and Varga SIAM J. Numer. Anal. 20 , 1170–1186 1983 ). Some illustrative numerical examples which show both the accuracy of the Gauss–Kronrod formulas and the sharpness of our estimations are displayed. Though for the sake of brevity we restrict ourselves to the first kind Chebyshev weight, a similar analysis may be carried out for the other three Chebyshev type weights; part of the corresponding computations are included in a final appendix.
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-022-01325-8