A new representation of generalized averaged Gauss quadrature rules
Apstrakt
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.
Ključne reči:
Generalized averaged Gauss rule / Gauss quadrature / Averaged Gauss ruleIzvor:
Applied Numerical Mathematics, 2021, 165, 614-619Izdavač:
- Elsevier, Amsterdam
Finansiranje / projekti:
- NSF [DMS-1720259, DMS1729509]
- Serbian Ministry of Education, Science and Technological Development and Science Fund of the Republic of Serbia
DOI: 10.1016/j.apnum.2020.11.016
ISSN: 0168-9274
WoS: 000634323600034
Scopus: 2-s2.0-85097092060
Kolekcije
Institucija/grupa
Mašinski fakultetTY - 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 . .