TY  - JOUR
AU  - Đukić, Dušan
AU  - Mutavdžić Đukić, Rada
AU  - Reichel, Lothar
AU  - Spalević, Miodrag
PY  - 2021
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3477
AB  - It is desirable that a quadrature rule be internal, i.e., that all nodes of the rule live in the convex hull of the support of the measure. Then the rule can be applied to approximate integrals of functions that have a singularity close to the convex hull of the support of the measure. This paper investigates whether generalized averaged Gauss quadrature formulas for modified Chebyshev measures of the first kind are internal. These rules are applied to estimate the error in Gauss quadrature rules associated with modified Chebyshev measures of the first kind. It is of considerable interest to be able to assess the error in quadrature rules in order to be able to choose a rule that gives an approximation of the desired integral of sufficient accuracy without having to evaluate the integrand at unnecessarily many nodes. Some of the generalized averaged Gauss quadrature formulas considered are found not to be internal. We will show that some truncated variants of these rules are internal, and therefore can be applied to estimate the error in Gauss quadrature rules also when the integrand has singularities on the real axis close to the interval of integration.
PB  - Elsevier, Amsterdam
T2  - Journal of Computational and Applied Mathematics
T1  - Internality of generalized averaged Gauss quadrature rules and truncated variants for modified Chebyshev measures of the first kind
VL  - 398
DO  - 10.1016/j.cam.2021.113696
ER  - 

@article{
author = "Đukić, Dušan and Mutavdžić Đukić, Rada and Reichel, Lothar and Spalević, Miodrag",
year = "2021",
abstract = "It is desirable that a quadrature rule be internal, i.e., that all nodes of the rule live in the convex hull of the support of the measure. Then the rule can be applied to approximate integrals of functions that have a singularity close to the convex hull of the support of the measure. This paper investigates whether generalized averaged Gauss quadrature formulas for modified Chebyshev measures of the first kind are internal. These rules are applied to estimate the error in Gauss quadrature rules associated with modified Chebyshev measures of the first kind. It is of considerable interest to be able to assess the error in quadrature rules in order to be able to choose a rule that gives an approximation of the desired integral of sufficient accuracy without having to evaluate the integrand at unnecessarily many nodes. Some of the generalized averaged Gauss quadrature formulas considered are found not to be internal. We will show that some truncated variants of these rules are internal, and therefore can be applied to estimate the error in Gauss quadrature rules also when the integrand has singularities on the real axis close to the interval of integration.",
publisher = "Elsevier, Amsterdam",
journal = "Journal of Computational and Applied Mathematics",
title = "Internality of generalized averaged Gauss quadrature rules and truncated variants for modified Chebyshev measures of the first kind",
volume = "398",
doi = "10.1016/j.cam.2021.113696"
}

Đukić, D., Mutavdžić Đukić, R., Reichel, L.,& Spalević, M.. (2021). Internality of generalized averaged Gauss quadrature rules and truncated variants for modified Chebyshev measures of the first kind. in Journal of Computational and Applied Mathematics
Elsevier, Amsterdam., 398.
https://doi.org/10.1016/j.cam.2021.113696

Đukić D, Mutavdžić Đukić R, Reichel L, Spalević M. Internality of generalized averaged Gauss quadrature rules and truncated variants for modified Chebyshev measures of the first kind. in Journal of Computational and Applied Mathematics. 2021;398.
doi:10.1016/j.cam.2021.113696 .

Đukić, Dušan, Mutavdžić Đukić, Rada, Reichel, Lothar, Spalević, Miodrag, "Internality of generalized averaged Gauss quadrature rules and truncated variants for modified Chebyshev measures of the first kind" in Journal of Computational and Applied Mathematics, 398 (2021),
https://doi.org/10.1016/j.cam.2021.113696 . .