Volume 50, pp. 20-35, 2018.

Error bounds for Kronrod extension of generalizations of Micchelli-Rivlin quadrature formula for analytic functions

Rada M. Mutavdžić, Aleksandar V. Pejčev, and Miodrag M. Spalević

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 $\mp 1$ and the sum of semi-axes $\rho >1$ for the mentioned quadrature formulas. We derive $L^{\mathrm{\infty }}$-error bounds and $L^1$-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.

Full Text (PDF) [322 KB], BibTeX , DOI: 10.1553/etna_vol50s20

Key words

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

AMS subject classifications

65D32, 65D30, 41A55

Links to the cited ETNA articles

[12]	Vol. 45 (2016), pp. 371-404 Sotirios E. Notaris: Gauss-Kronrod quadrature formulae - A survey of fifty years of research

ETNA articles which cite this article

Vol. 53 (2020), pp. 352-382 D. Lj. Djukić, R. M. Mutavdžić Djukić, A. V. Pejčev, and M. M. Spalević: Error estimates of Gaussian-type quadrature formulae for analytic functions on ellipses-a survey of recent results