Cubature formulae for the gaussian weight. Some old and new rules.
Апстракт
In this paper we review some of the main known facts about cubature rules to approximate integrals over domains in R-n, in particular with respect to the Gaussian weight w(x) = e(-xTx); where x = (x(1); ... ; x(n)) is an element of R-n. Some new rules are also presented. Taking into account the well-known issue of the "curse of dimensionality", our aim is at providing rules with a certain degree of algebraic precision and a reasonably small number of nodes as well as an acceptable stability. We think that the methods used to construct these new rules are of further applicability in the field of cubature formulas. The efficiency of new and old rules are compared by means of several numerical experiments.
Кључне речи:
Gaussian weight / cubature formulasИзвор:
Electronic Transactions on Numerical Analysis, 2020, 53, 426-438Издавач:
- Kent State University, Kent
Финансирање / пројекти:
- Ministerio de Ciencia e Innovacion [MTM2015-71352-P
- Министарство науке, технолошког развоја и иновација Републике Србије, институционално финансирање - 200105 (Универзитет у Београду, Машински факултет) (RS-200105)
DOI: 10.1553/etna_vol53s426
ISSN: 1068-9613
WoS: 000605216800012
Scopus: 2-s2.0-85087334985
Колекције
Институција/група
Mašinski fakultetTY - JOUR AU - Orive, Ramon AU - Santos-Leon, Juan C. AU - Spalević, Miodrag PY - 2020 UR - https://machinery.mas.bg.ac.rs/handle/123456789/3282 AB - In this paper we review some of the main known facts about cubature rules to approximate integrals over domains in R-n, in particular with respect to the Gaussian weight w(x) = e(-xTx); where x = (x(1); ... ; x(n)) is an element of R-n. Some new rules are also presented. Taking into account the well-known issue of the "curse of dimensionality", our aim is at providing rules with a certain degree of algebraic precision and a reasonably small number of nodes as well as an acceptable stability. We think that the methods used to construct these new rules are of further applicability in the field of cubature formulas. The efficiency of new and old rules are compared by means of several numerical experiments. PB - Kent State University, Kent T2 - Electronic Transactions on Numerical Analysis T1 - Cubature formulae for the gaussian weight. Some old and new rules. EP - 438 SP - 426 VL - 53 DO - 10.1553/etna_vol53s426 ER -
@article{ author = "Orive, Ramon and Santos-Leon, Juan C. and Spalević, Miodrag", year = "2020", abstract = "In this paper we review some of the main known facts about cubature rules to approximate integrals over domains in R-n, in particular with respect to the Gaussian weight w(x) = e(-xTx); where x = (x(1); ... ; x(n)) is an element of R-n. Some new rules are also presented. Taking into account the well-known issue of the "curse of dimensionality", our aim is at providing rules with a certain degree of algebraic precision and a reasonably small number of nodes as well as an acceptable stability. We think that the methods used to construct these new rules are of further applicability in the field of cubature formulas. The efficiency of new and old rules are compared by means of several numerical experiments.", publisher = "Kent State University, Kent", journal = "Electronic Transactions on Numerical Analysis", title = "Cubature formulae for the gaussian weight. Some old and new rules.", pages = "438-426", volume = "53", doi = "10.1553/etna_vol53s426" }
Orive, R., Santos-Leon, J. C.,& Spalević, M.. (2020). Cubature formulae for the gaussian weight. Some old and new rules.. in Electronic Transactions on Numerical Analysis Kent State University, Kent., 53, 426-438. https://doi.org/10.1553/etna_vol53s426
Orive R, Santos-Leon JC, Spalević M. Cubature formulae for the gaussian weight. Some old and new rules.. in Electronic Transactions on Numerical Analysis. 2020;53:426-438. doi:10.1553/etna_vol53s426 .
Orive, Ramon, Santos-Leon, Juan C., Spalević, Miodrag, "Cubature formulae for the gaussian weight. Some old and new rules." in Electronic Transactions on Numerical Analysis, 53 (2020):426-438, https://doi.org/10.1553/etna_vol53s426 . .