TY - JOUR
T1 - Simple Fourth-Degree Cubature Formulae with Few Nodes over General Product Regions
AU - Ran Yu, Zhaoliang Meng & Zhongxuan Luo
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 - <p style="text-align: justify;">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.</p>