TY  - JOUR
AU  - Reichel, Lothar
AU  - Spalević, Miodrag
PY  - 2021
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3597
AB  - Gauss quadrature rules associated with a nonnegative measure with support on (part of) the real axis find many applications in Scientific Computing. It is important to be able to estimate the quadrature error when replacing an integral by an l-node Gauss quadrature rule in order to choose a suitable number of nodes. A classical approach to estimate this error is to evaluate the associated (2l + 1)-node Gauss-Kronrod rule. However, Gauss-Kronrod rules with 2l + 1 real nodes might not exist. The (2l + 1)-node generalized averaged Gauss formula associated with the l-node Gauss rule described in Spalevic (2007) [16] is guaranteed to exist and provides an attractive alternative to the (2l + 1)-node Gauss-Kronrod rule. This paper describes a new representation of generalized averaged Gauss formulas that is cheaper to evaluate than the available representation.
PB  - Elsevier, Amsterdam
T2  - Applied Numerical Mathematics
T1  - A new representation of generalized averaged Gauss quadrature rules
EP  - 619
SP  - 614
VL  - 165
DO  - 10.1016/j.apnum.2020.11.016
ER  - 

@article{
author = "Reichel, Lothar and Spalević, Miodrag",
year = "2021",
abstract = "Gauss quadrature rules associated with a nonnegative measure with support on (part of) the real axis find many applications in Scientific Computing. It is important to be able to estimate the quadrature error when replacing an integral by an l-node Gauss quadrature rule in order to choose a suitable number of nodes. A classical approach to estimate this error is to evaluate the associated (2l + 1)-node Gauss-Kronrod rule. However, Gauss-Kronrod rules with 2l + 1 real nodes might not exist. The (2l + 1)-node generalized averaged Gauss formula associated with the l-node Gauss rule described in Spalevic (2007) [16] is guaranteed to exist and provides an attractive alternative to the (2l + 1)-node Gauss-Kronrod rule. This paper describes a new representation of generalized averaged Gauss formulas that is cheaper to evaluate than the available representation.",
publisher = "Elsevier, Amsterdam",
journal = "Applied Numerical Mathematics",
title = "A new representation of generalized averaged Gauss quadrature rules",
pages = "619-614",
volume = "165",
doi = "10.1016/j.apnum.2020.11.016"
}

Reichel, L.,& Spalević, M.. (2021). A new representation of generalized averaged Gauss quadrature rules. in Applied Numerical Mathematics
Elsevier, Amsterdam., 165, 614-619.
https://doi.org/10.1016/j.apnum.2020.11.016

Reichel L, Spalević M. A new representation of generalized averaged Gauss quadrature rules. in Applied Numerical Mathematics. 2021;165:614-619.
doi:10.1016/j.apnum.2020.11.016 .

Reichel, Lothar, Spalević, Miodrag, "A new representation of generalized averaged Gauss quadrature rules" in Applied Numerical Mathematics, 165 (2021):614-619,
https://doi.org/10.1016/j.apnum.2020.11.016 . .