@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} }