Simple Fourth-Degree Cubature Formulae with Few Nodes over General Product Regions. Issue 2 (May 2014) - Yu, Ran; Meng, Zhaoliang; Luo, Zhongxuan
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 + 7 n + 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.