Error estimates of gaussian quadrature formulae with the third class of bernstein-szego weights
Апстракт
For analytic functions we study the remainder terms of Gauss quadrature rules with respect to Bernstein-Szego weight functions w(t) = w(alpha,beta,delta)(t) = root 1+t/1-t/beta(beta-2 alpha)t(2) + 2 delta(beta-alpha)t+alpha(2) + delta(2) , t epsilon(-1,1), where 0 lt alpha lt beta, beta not equal 2 alpha, vertical bar delta vertical bar lt beta-alpha, and whose denominator is an arbitrary polynomial of exact degree 2 that remains positive on [-1,1]. The subcase alpha = 1, beta = 2/(1 + gamma), -1 lt gamma lt 0 and delta = 0 has been considered recently by M. M. Spalevie, Error bounds of Gaussian quadrature formulae for one class of Bernstein-Szego weights, Math. Comp., 82 (2013), 1037-1056.
Кључне речи:
remainder term / Gauss quadrature / error bound / elliptic contour / analytic functionИзвор:
Applicable Analysis and Discrete Mathematics, 2017, 11, 2, 451-469Издавач:
- Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd
Финансирање / пројекти:
- Методе нумеричке и нелинеарне анализе са применама (RS-MESTD-Basic Research (BR or ON)-174002)
DOI: 10.2298/AADM1702451P
ISSN: 1452-8630
WoS: 000414668600015
Scopus: 2-s2.0-85031905343
Колекције
Институција/група
Mašinski fakultetTY - JOUR AU - Pejčev, Aleksandar PY - 2017 UR - https://machinery.mas.bg.ac.rs/handle/123456789/2509 AB - For analytic functions we study the remainder terms of Gauss quadrature rules with respect to Bernstein-Szego weight functions w(t) = w(alpha,beta,delta)(t) = root 1+t/1-t/beta(beta-2 alpha)t(2) + 2 delta(beta-alpha)t+alpha(2) + delta(2) , t epsilon(-1,1), where 0 lt alpha lt beta, beta not equal 2 alpha, vertical bar delta vertical bar lt beta-alpha, and whose denominator is an arbitrary polynomial of exact degree 2 that remains positive on [-1,1]. The subcase alpha = 1, beta = 2/(1 + gamma), -1 lt gamma lt 0 and delta = 0 has been considered recently by M. M. Spalevie, Error bounds of Gaussian quadrature formulae for one class of Bernstein-Szego weights, Math. Comp., 82 (2013), 1037-1056. PB - Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd T2 - Applicable Analysis and Discrete Mathematics T1 - Error estimates of gaussian quadrature formulae with the third class of bernstein-szego weights EP - 469 IS - 2 SP - 451 VL - 11 DO - 10.2298/AADM1702451P ER -
@article{ author = "Pejčev, Aleksandar", year = "2017", abstract = "For analytic functions we study the remainder terms of Gauss quadrature rules with respect to Bernstein-Szego weight functions w(t) = w(alpha,beta,delta)(t) = root 1+t/1-t/beta(beta-2 alpha)t(2) + 2 delta(beta-alpha)t+alpha(2) + delta(2) , t epsilon(-1,1), where 0 lt alpha lt beta, beta not equal 2 alpha, vertical bar delta vertical bar lt beta-alpha, and whose denominator is an arbitrary polynomial of exact degree 2 that remains positive on [-1,1]. The subcase alpha = 1, beta = 2/(1 + gamma), -1 lt gamma lt 0 and delta = 0 has been considered recently by M. M. Spalevie, Error bounds of Gaussian quadrature formulae for one class of Bernstein-Szego weights, Math. Comp., 82 (2013), 1037-1056.", publisher = "Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd", journal = "Applicable Analysis and Discrete Mathematics", title = "Error estimates of gaussian quadrature formulae with the third class of bernstein-szego weights", pages = "469-451", number = "2", volume = "11", doi = "10.2298/AADM1702451P" }
Pejčev, A.. (2017). Error estimates of gaussian quadrature formulae with the third class of bernstein-szego weights. in Applicable Analysis and Discrete Mathematics Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd., 11(2), 451-469. https://doi.org/10.2298/AADM1702451P
Pejčev A. Error estimates of gaussian quadrature formulae with the third class of bernstein-szego weights. in Applicable Analysis and Discrete Mathematics. 2017;11(2):451-469. doi:10.2298/AADM1702451P .
Pejčev, Aleksandar, "Error estimates of gaussian quadrature formulae with the third class of bernstein-szego weights" in Applicable Analysis and Discrete Mathematics, 11, no. 2 (2017):451-469, https://doi.org/10.2298/AADM1702451P . .