The error bounds of gauss-lobatto quadratures for weights ofbernstein-szego type
Apstrakt
In this paper, we consider the Gauss-Lobatto quadrature formulas for the Bernstein-Szego weights, i.e., any of the four Chebyshev weights divided by a polynomial of the form rho(t) = 1 - 4 gamma/(1+gamma)(2) t(2), where t is an element of (-1,1) and gamma is an element of (-1,0]. Our objective is to study the kernel in the contour integral representation of the remainder term and to locate the points on elliptic contours where the modulus of the kernel is maximal. We use this to derive the error bounds for mentioned quadrature formulas.
Ključne reči:
remainder term for analytic functions / Gauss-Lobatto quadrature formula / error bound / contour integral representation / Bernstein-Szego weight functionsIzvor:
Applicable Analysis and Discrete Mathematics, 2019, 13, 3, 733-745Izdavač:
- Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd
Finansiranje / projekti:
- Metode numeričke i nelinearne analize sa primenama (RS-MESTD-Basic Research (BR or ON)-174002)
DOI: 10.2298/AADM190315030M
ISSN: 1452-8630
WoS: 000503720000006
Scopus: 2-s2.0-85080941709
Kolekcije
Institucija/grupa
Mašinski fakultetTY - JOUR AU - Mutavdžić Đukić, Rada AU - Pejčev, Aleksandar AU - Spalević, Miodrag PY - 2019 UR - https://machinery.mas.bg.ac.rs/handle/123456789/3037 AB - In this paper, we consider the Gauss-Lobatto quadrature formulas for the Bernstein-Szego weights, i.e., any of the four Chebyshev weights divided by a polynomial of the form rho(t) = 1 - 4 gamma/(1+gamma)(2) t(2), where t is an element of (-1,1) and gamma is an element of (-1,0]. Our objective is to study the kernel in the contour integral representation of the remainder term and to locate the points on elliptic contours where the modulus of the kernel is maximal. We use this to derive the error bounds for mentioned quadrature formulas. PB - Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd T2 - Applicable Analysis and Discrete Mathematics T1 - The error bounds of gauss-lobatto quadratures for weights ofbernstein-szego type EP - 745 IS - 3 SP - 733 VL - 13 DO - 10.2298/AADM190315030M ER -
@article{ author = "Mutavdžić Đukić, Rada and Pejčev, Aleksandar and Spalević, Miodrag", year = "2019", abstract = "In this paper, we consider the Gauss-Lobatto quadrature formulas for the Bernstein-Szego weights, i.e., any of the four Chebyshev weights divided by a polynomial of the form rho(t) = 1 - 4 gamma/(1+gamma)(2) t(2), where t is an element of (-1,1) and gamma is an element of (-1,0]. Our objective is to study the kernel in the contour integral representation of the remainder term and to locate the points on elliptic contours where the modulus of the kernel is maximal. We use this to derive the error bounds for mentioned quadrature formulas.", publisher = "Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd", journal = "Applicable Analysis and Discrete Mathematics", title = "The error bounds of gauss-lobatto quadratures for weights ofbernstein-szego type", pages = "745-733", number = "3", volume = "13", doi = "10.2298/AADM190315030M" }
Mutavdžić Đukić, R., Pejčev, A.,& Spalević, M.. (2019). The error bounds of gauss-lobatto quadratures for weights ofbernstein-szego type. in Applicable Analysis and Discrete Mathematics Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd., 13(3), 733-745. https://doi.org/10.2298/AADM190315030M
Mutavdžić Đukić R, Pejčev A, Spalević M. The error bounds of gauss-lobatto quadratures for weights ofbernstein-szego type. in Applicable Analysis and Discrete Mathematics. 2019;13(3):733-745. doi:10.2298/AADM190315030M .
Mutavdžić Đukić, Rada, Pejčev, Aleksandar, Spalević, Miodrag, "The error bounds of gauss-lobatto quadratures for weights ofbernstein-szego type" in Applicable Analysis and Discrete Mathematics, 13, no. 3 (2019):733-745, https://doi.org/10.2298/AADM190315030M . .