Rada M. Mutavdžić,
Aleksandar V. Pejčev,
Miodrag M. Spalević
S. 20 - 35
doi:
10.1553/etna_vol50s20
Verlag der Österreichischen Akademie der Wissenschaften
doi:
10.1553/etna_vol50s20
Abstract:
We consider the Kronrod extension of generalizations of the Micchelli-Rivlin quadrature formula for the Fourier-Chebyshev coefficients with the highest algebraic degree of precision. For analytic functions, the remainder term of these quadrature formulas can be represented as a contour integral with a complex kernel. We study the kernel on elliptic contours with foci at the points ∓1 and the sum of semi-axes ρ>1 for the mentioned quadrature formulas. We derive L∞-error bounds and L1-error bounds for these quadrature formulas. Finally, we obtain explicit bounds by expanding the remainder term. Numerical examples that compare these error bounds are included.
Kronrod extension of generalizations of the Micchelli-Rivlin quadrature formula, Chebyshev weight function of the first kind, error bound, remainder term for analytic functions, contour integral representation
Published Online:
2018/11/12 09:48:44
Object Identifier:
0xc1aa5576 0x003a0b08
Rights:All rights reserved.For questions regarding copyright and copies please contact us by email.
Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613.
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