Error bounds for kronrod extension of generalizations of micchelli-rivlin quadrature formula for analytic functions
Апстракт
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 rho > 1 for the mentioned quadrature formulas. We derive L-infinity-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.
Кључне речи:
remainder term for analytic functions / Kronrod extension of generalizations of the Micchelli-Rivlin quadrature formula / error bound / contour integral representation / Chebyshev weight function of the first kindИзвор:
Electronic Transactions on Numerical Analysis, 2018, 50, 20-35Издавач:
- Kent State University
Финансирање / пројекти:
- Методе нумеричке и нелинеарне анализе са применама (RS-MESTD-Basic Research (BR or ON)-174002)
DOI: 10.1553/etna-vol50s20
ISSN: 1068-9613
WoS: 000459296200003
Scopus: 2-s2.0-85058243095
Колекције
Институција/група
Mašinski fakultetTY - JOUR AU - Mutavdžić Đukić, Rada AU - Pejčev, Aleksandar AU - Spalević, Miodrag PY - 2018 UR - https://machinery.mas.bg.ac.rs/handle/123456789/2954 AB - 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 rho > 1 for the mentioned quadrature formulas. We derive L-infinity-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. PB - Kent State University T2 - Electronic Transactions on Numerical Analysis T1 - Error bounds for kronrod extension of generalizations of micchelli-rivlin quadrature formula for analytic functions EP - 35 SP - 20 VL - 50 DO - 10.1553/etna-vol50s20 ER -
@article{ author = "Mutavdžić Đukić, Rada and Pejčev, Aleksandar and Spalević, Miodrag", year = "2018", 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 rho > 1 for the mentioned quadrature formulas. We derive L-infinity-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.", publisher = "Kent State University", journal = "Electronic Transactions on Numerical Analysis", title = "Error bounds for kronrod extension of generalizations of micchelli-rivlin quadrature formula for analytic functions", pages = "35-20", volume = "50", doi = "10.1553/etna-vol50s20" }
Mutavdžić Đukić, R., Pejčev, A.,& Spalević, M.. (2018). Error bounds for kronrod extension of generalizations of micchelli-rivlin quadrature formula for analytic functions. in Electronic Transactions on Numerical Analysis Kent State University., 50, 20-35. https://doi.org/10.1553/etna-vol50s20
Mutavdžić Đukić R, Pejčev A, Spalević M. Error bounds for kronrod extension of generalizations of micchelli-rivlin quadrature formula for analytic functions. in Electronic Transactions on Numerical Analysis. 2018;50:20-35. doi:10.1553/etna-vol50s20 .
Mutavdžić Đukić, Rada, Pejčev, Aleksandar, Spalević, Miodrag, "Error bounds for kronrod extension of generalizations of micchelli-rivlin quadrature formula for analytic functions" in Electronic Transactions on Numerical Analysis, 50 (2018):20-35, https://doi.org/10.1553/etna-vol50s20 . .