Error estimates of anti-Gaussian quadrature formulae
Апстракт
Anti-Gauss quadrature formulae associated with four classical Chebyshev weight functions are considered. Complex-variable methods are used to obtain expansions of the error in anti-Gaussian quadrature formulae over the interval vertical bar-1, 1 vertical bar. The kernel of the remainder term in anti-Gaussian quadrature formulae is analyzed. The location on the elliptic contours where the modulus of the kernel attains its maximum value is investigated. This leads to effective L-infinity-error bounds of anti-Gauss quadratures. Moreover, the effective L-1-error estimates are also derived. The results obtained here are an analogue of some results of Gautschi and Varga (1983) [11], Gautschi et al. (1990) [9] and Hunter (1995) [10] concerning Gaussian quadratures.
Кључне речи:
Remainder term / Error estimate / Elliptic contour / Anti-Gauss quadratureИзвор:
Journal of Computational and Applied Mathematics, 2012, 236, 15, 3542-3555Издавач:
- Elsevier Science Bv, Amsterdam
Финансирање / пројекти:
- Методе нумеричке и нелинеарне анализе са применама (RS-MESTD-Basic Research (BR or ON)-174002)
DOI: 10.1016/j.cam.2011.03.026
ISSN: 0377-0427
WoS: 000305360000002
Scopus: 2-s2.0-84861527921
Колекције
Институција/група
Mašinski fakultetTY - JOUR AU - Spalević, Miodrag PY - 2012 UR - https://machinery.mas.bg.ac.rs/handle/123456789/1487 AB - Anti-Gauss quadrature formulae associated with four classical Chebyshev weight functions are considered. Complex-variable methods are used to obtain expansions of the error in anti-Gaussian quadrature formulae over the interval vertical bar-1, 1 vertical bar. The kernel of the remainder term in anti-Gaussian quadrature formulae is analyzed. The location on the elliptic contours where the modulus of the kernel attains its maximum value is investigated. This leads to effective L-infinity-error bounds of anti-Gauss quadratures. Moreover, the effective L-1-error estimates are also derived. The results obtained here are an analogue of some results of Gautschi and Varga (1983) [11], Gautschi et al. (1990) [9] and Hunter (1995) [10] concerning Gaussian quadratures. PB - Elsevier Science Bv, Amsterdam T2 - Journal of Computational and Applied Mathematics T1 - Error estimates of anti-Gaussian quadrature formulae EP - 3555 IS - 15 SP - 3542 VL - 236 DO - 10.1016/j.cam.2011.03.026 ER -
@article{ author = "Spalević, Miodrag", year = "2012", abstract = "Anti-Gauss quadrature formulae associated with four classical Chebyshev weight functions are considered. Complex-variable methods are used to obtain expansions of the error in anti-Gaussian quadrature formulae over the interval vertical bar-1, 1 vertical bar. The kernel of the remainder term in anti-Gaussian quadrature formulae is analyzed. The location on the elliptic contours where the modulus of the kernel attains its maximum value is investigated. This leads to effective L-infinity-error bounds of anti-Gauss quadratures. Moreover, the effective L-1-error estimates are also derived. The results obtained here are an analogue of some results of Gautschi and Varga (1983) [11], Gautschi et al. (1990) [9] and Hunter (1995) [10] concerning Gaussian quadratures.", publisher = "Elsevier Science Bv, Amsterdam", journal = "Journal of Computational and Applied Mathematics", title = "Error estimates of anti-Gaussian quadrature formulae", pages = "3555-3542", number = "15", volume = "236", doi = "10.1016/j.cam.2011.03.026" }
Spalević, M.. (2012). Error estimates of anti-Gaussian quadrature formulae. in Journal of Computational and Applied Mathematics Elsevier Science Bv, Amsterdam., 236(15), 3542-3555. https://doi.org/10.1016/j.cam.2011.03.026
Spalević M. Error estimates of anti-Gaussian quadrature formulae. in Journal of Computational and Applied Mathematics. 2012;236(15):3542-3555. doi:10.1016/j.cam.2011.03.026 .
Spalević, Miodrag, "Error estimates of anti-Gaussian quadrature formulae" in Journal of Computational and Applied Mathematics, 236, no. 15 (2012):3542-3555, https://doi.org/10.1016/j.cam.2011.03.026 . .