Volume 7, Issue 2
Simple Fourth-Degree Cubature Formulae with Few Nodes over General Product Regions

Ran Yu, Zhaoliang Meng & Zhongxuan Luo

Numer. Math. Theor. Meth. Appl., 7 (2014), pp. 179-192.

Published online: 2014-07

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  • Abstract

A simple method is proposed for constructing fourth-degree cubature formulae over general product regions with no symmetric assumptions. The cubature formulae that are constructed contain at most $n^2+7n+3$ nodes and they are likely the first kind of fourth-degree cubature formulae with roughly $n^2$ nodes for non-symmetric integrations. Moreover, two special cases are given to reduce the number of nodes further. A theoretical upper bound for minimal number of cubature nodes is also obtained.

  • Keywords

Fourth-degree cubature formula, cubature formula, product region, non-symmetric region, numerical integration.

  • AMS Subject Headings

65D30, 65D32

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-7-179, author = {}, title = {Simple Fourth-Degree Cubature Formulae with Few Nodes over General Product Regions}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2014}, volume = {7}, number = {2}, pages = {179--192}, abstract = {

A simple method is proposed for constructing fourth-degree cubature formulae over general product regions with no symmetric assumptions. The cubature formulae that are constructed contain at most $n^2+7n+3$ nodes and they are likely the first kind of fourth-degree cubature formulae with roughly $n^2$ nodes for non-symmetric integrations. Moreover, two special cases are given to reduce the number of nodes further. A theoretical upper bound for minimal number of cubature nodes is also obtained.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2014.y12038}, url = {http://global-sci.org/intro/article_detail/nmtma/5870.html} }
TY - JOUR T1 - Simple Fourth-Degree Cubature Formulae with Few Nodes over General Product Regions JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 179 EP - 192 PY - 2014 DA - 2014/07 SN - 7 DO - http://doi.org/10.4208/nmtma.2014.y12038 UR - https://global-sci.org/intro/article_detail/nmtma/5870.html KW - Fourth-degree cubature formula, cubature formula, product region, non-symmetric region, numerical integration. AB -

A simple method is proposed for constructing fourth-degree cubature formulae over general product regions with no symmetric assumptions. The cubature formulae that are constructed contain at most $n^2+7n+3$ nodes and they are likely the first kind of fourth-degree cubature formulae with roughly $n^2$ nodes for non-symmetric integrations. Moreover, two special cases are given to reduce the number of nodes further. A theoretical upper bound for minimal number of cubature nodes is also obtained.

Ran Yu, Zhaoliang Meng & Zhongxuan Luo. (2020). Simple Fourth-Degree Cubature Formulae with Few Nodes over General Product Regions. Numerical Mathematics: Theory, Methods and Applications. 7 (2). 179-192. doi:10.4208/nmtma.2014.y12038
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