Error bounds for Kronrod extension of generalizations of Micchelli-Rivlin quadrature formula for analytic functions. ETNA - Electronic Transactions on Numerical Analysis
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12 novembre 2018
- handle: 10670/1.1z8ku8
- issn: 1068-9613
- doi: 10.1553/etna_vol50s20
info:eu-repo/semantics/openAccess
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Aleksandar V. Pejčev et al., « Error bounds for Kronrod extension of generalizations of Micchelli-Rivlin quadrature formula for analytic functions. ETNA - Electronic Transactions on Numerical Analysis », Elektronisches Publikationsportal der Österreichischen Akademie der Wissenschafte, ID : 10.1553/etna_vol50s20
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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.