Simple Fourth-Degree Cubature Formulae with Few Nodes over General Product Regions

作     者：Ran Yu Zhaoliang Meng Zhongxuan Luo 

作者机构：School of Mathematical SciencesDalian University of TechnologyDalian116024P.R.China School of SoftwareDalian University of TechnologyDalian116620P.R.China 

出 版 物：《Numerical Mathematics(Theory,Methods and Applications)》 (高等学校计算数学学报（英文版）)

年 卷 期：2014年第7卷第2期

页      面：179-192页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：This research is supported by the National Natural Science Foundation of China(Grant Nos.61033012,11301153,10771028) “the Fundamental Research Funds for the Central Universities” 

主　　题：Fourth-degree cubature formula cubature formula product region non-symmetric region numerical integration 

摘      要：A simple method is proposed for constructing fourth-degree cubature formulae over general product regions with no symmetric assumptions. The cubatureformulae that are constructed contain at most n2 + 7n + 3 nodes and they are likelythe first kind of fourth-degree cubature formulae with roughly n2 nodes for nonsymmetric integrations. Moreover, two special cases are given to reduce the numberof nodes further. A theoretical upper bound for minimal number of cubature nodesis also obtained.