Internality of averaged Gauss quadrature rules for certain modification of Jacobi measures
Апстракт
The internality of quadrature rules, i.e., the property that all nodes lie in the interior of the convex hull of the support of the measure, is important in applications, because this allows the application of these quadrature rules to the approximation of integrals with integrands that are defined in the convex hull of the support of the measure only. It is known that the averaged Gauss and optimal averaged Gauss quadrature rules with respect to the four Chebyshev measures modified by a linear divisor are internal. This paper investigates the internality of similarly modified Jacobi measures, namely measures defined by weight functions. With a, b > −1 and z ∈ R, |z| > 1. We will show that in some cases, depending on the exponents a and b, the averaged and optimal averaged Gauss rules for these measures are internal if the number of nodes is large enough.
Кључне речи:
Gauss Quadrature / Generalized Averaged Gauss Quadrature / Truncated Generalized Averaged Gauss Quadrature / Internality of Quadrature Rule / Modified Jacobi MeasureИзвор:
Applied and Computational Mathematics, 2023, 22, 4, 426-442Издавач:
- Ministry of Communications and Information Technology (Azerbaijan), Azerbaijan National Academy of Sciences and Institute of Applied Mathematics of Baku State University
Финансирање / пројекти:
- Министарство науке, технолошког развоја и иновација Републике Србије, институционално финансирање - 200105 (Универзитет у Београду, Машински факултет) (RS-MESTD-inst-2020-200105)
URI
http://acmij.az/view.php?lang=az&menu=0http://acmij.az/view.php?lang=az&menu=journal&id=624
https://machinery.mas.bg.ac.rs/handle/123456789/7380
Колекције
Институција/група
Mašinski fakultetTY - JOUR AU - Đukić, Dušan AU - Mutavdžić Đukić, Rada AU - Reichel, Lothar AU - Spalević, Miodrag PY - 2023 UR - http://acmij.az/view.php?lang=az&menu=0 UR - http://acmij.az/view.php?lang=az&menu=journal&id=624 UR - https://machinery.mas.bg.ac.rs/handle/123456789/7380 AB - The internality of quadrature rules, i.e., the property that all nodes lie in the interior of the convex hull of the support of the measure, is important in applications, because this allows the application of these quadrature rules to the approximation of integrals with integrands that are defined in the convex hull of the support of the measure only. It is known that the averaged Gauss and optimal averaged Gauss quadrature rules with respect to the four Chebyshev measures modified by a linear divisor are internal. This paper investigates the internality of similarly modified Jacobi measures, namely measures defined by weight functions. With a, b > −1 and z ∈ R, |z| > 1. We will show that in some cases, depending on the exponents a and b, the averaged and optimal averaged Gauss rules for these measures are internal if the number of nodes is large enough. PB - Ministry of Communications and Information Technology (Azerbaijan), Azerbaijan National Academy of Sciences and Institute of Applied Mathematics of Baku State University T2 - Applied and Computational Mathematics T1 - Internality of averaged Gauss quadrature rules for certain modification of Jacobi measures EP - 442 IS - 4 SP - 426 VL - 22 DO - 10.30546/1683-6154.22.4.2023.426 ER -
@article{ author = "Đukić, Dušan and Mutavdžić Đukić, Rada and Reichel, Lothar and Spalević, Miodrag", year = "2023", abstract = "The internality of quadrature rules, i.e., the property that all nodes lie in the interior of the convex hull of the support of the measure, is important in applications, because this allows the application of these quadrature rules to the approximation of integrals with integrands that are defined in the convex hull of the support of the measure only. It is known that the averaged Gauss and optimal averaged Gauss quadrature rules with respect to the four Chebyshev measures modified by a linear divisor are internal. This paper investigates the internality of similarly modified Jacobi measures, namely measures defined by weight functions. With a, b > −1 and z ∈ R, |z| > 1. We will show that in some cases, depending on the exponents a and b, the averaged and optimal averaged Gauss rules for these measures are internal if the number of nodes is large enough.", publisher = "Ministry of Communications and Information Technology (Azerbaijan), Azerbaijan National Academy of Sciences and Institute of Applied Mathematics of Baku State University", journal = "Applied and Computational Mathematics", title = "Internality of averaged Gauss quadrature rules for certain modification of Jacobi measures", pages = "442-426", number = "4", volume = "22", doi = "10.30546/1683-6154.22.4.2023.426" }
Đukić, D., Mutavdžić Đukić, R., Reichel, L.,& Spalević, M.. (2023). Internality of averaged Gauss quadrature rules for certain modification of Jacobi measures. in Applied and Computational Mathematics Ministry of Communications and Information Technology (Azerbaijan), Azerbaijan National Academy of Sciences and Institute of Applied Mathematics of Baku State University., 22(4), 426-442. https://doi.org/10.30546/1683-6154.22.4.2023.426
Đukić D, Mutavdžić Đukić R, Reichel L, Spalević M. Internality of averaged Gauss quadrature rules for certain modification of Jacobi measures. in Applied and Computational Mathematics. 2023;22(4):426-442. doi:10.30546/1683-6154.22.4.2023.426 .
Đukić, Dušan, Mutavdžić Đukić, Rada, Reichel, Lothar, Spalević, Miodrag, "Internality of averaged Gauss quadrature rules for certain modification of Jacobi measures" in Applied and Computational Mathematics, 22, no. 4 (2023):426-442, https://doi.org/10.30546/1683-6154.22.4.2023.426 . .
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