Error estimates for Gaussian quadratures of analytic functions
Апстракт
For analytic functions the remainder term of Gaussian quadrature formula and its Kronrod extension can be represented as a contour integral with a complex kernel. We study these kernels on elliptic contours with foci at the points +/-1 and the sum of semi-axes Q > 1 for the Chebyshev weight functions of the first, second and third kind, and derive representation of their difference. Using this representation and following Kronrod's method of obtaining a practical error estimate in numerical integration, we derive new error estimates for Gaussian quadratures.
Кључне речи:
Remainder term for analytic functions / Gaussian quadrature formula / Error bound / Contour integral representation / Chebyshev weight functionИзвор:
Journal of Computational and Applied Mathematics, 2009, 233, 3, 802-807Издавач:
- Elsevier Science Bv, Amsterdam
DOI: 10.1016/j.cam.2009.02.048
ISSN: 0377-0427
WoS: 000271346000029
Scopus: 2-s2.0-69749112956
Колекције
Институција/група
Mašinski fakultetTY - JOUR AU - Milovanović, Gradimir V. AU - Spalević, Miodrag AU - Pranić, Miroslav S. PY - 2009 UR - https://machinery.mas.bg.ac.rs/handle/123456789/969 AB - For analytic functions the remainder term of Gaussian quadrature formula and its Kronrod extension can be represented as a contour integral with a complex kernel. We study these kernels on elliptic contours with foci at the points +/-1 and the sum of semi-axes Q > 1 for the Chebyshev weight functions of the first, second and third kind, and derive representation of their difference. Using this representation and following Kronrod's method of obtaining a practical error estimate in numerical integration, we derive new error estimates for Gaussian quadratures. PB - Elsevier Science Bv, Amsterdam T2 - Journal of Computational and Applied Mathematics T1 - Error estimates for Gaussian quadratures of analytic functions EP - 807 IS - 3 SP - 802 VL - 233 DO - 10.1016/j.cam.2009.02.048 ER -
@article{ author = "Milovanović, Gradimir V. and Spalević, Miodrag and Pranić, Miroslav S.", year = "2009", abstract = "For analytic functions the remainder term of Gaussian quadrature formula and its Kronrod extension can be represented as a contour integral with a complex kernel. We study these kernels on elliptic contours with foci at the points +/-1 and the sum of semi-axes Q > 1 for the Chebyshev weight functions of the first, second and third kind, and derive representation of their difference. Using this representation and following Kronrod's method of obtaining a practical error estimate in numerical integration, we derive new error estimates for Gaussian quadratures.", publisher = "Elsevier Science Bv, Amsterdam", journal = "Journal of Computational and Applied Mathematics", title = "Error estimates for Gaussian quadratures of analytic functions", pages = "807-802", number = "3", volume = "233", doi = "10.1016/j.cam.2009.02.048" }
Milovanović, G. V., Spalević, M.,& Pranić, M. S.. (2009). Error estimates for Gaussian quadratures of analytic functions. in Journal of Computational and Applied Mathematics Elsevier Science Bv, Amsterdam., 233(3), 802-807. https://doi.org/10.1016/j.cam.2009.02.048
Milovanović GV, Spalević M, Pranić MS. Error estimates for Gaussian quadratures of analytic functions. in Journal of Computational and Applied Mathematics. 2009;233(3):802-807. doi:10.1016/j.cam.2009.02.048 .
Milovanović, Gradimir V., Spalević, Miodrag, Pranić, Miroslav S., "Error estimates for Gaussian quadratures of analytic functions" in Journal of Computational and Applied Mathematics, 233, no. 3 (2009):802-807, https://doi.org/10.1016/j.cam.2009.02.048 . .