In this paper,matrix representations of the best spline quasi-interpolating operator over triangular sub-domains in S_(2)^(1)(△_(mn)^(2),and coefficients of splines in terms of B-net are calculated firstly.Moreover,b...In this paper,matrix representations of the best spline quasi-interpolating operator over triangular sub-domains in S_(2)^(1)(△_(mn)^(2),and coefficients of splines in terms of B-net are calculated firstly.Moreover,by means of coefficients in terms of B-net,computation of bivariate numerical cubature over triangular sub-domains with respect to variables x and y is transferred into summation of coefficients of splines in terms of B-net.Thus concise bivariate cubature formulas are constructed over rectangular sub-domain.Furthermore,by means of module of continuity and max-norms,error estimates for cubature formulas are derived over both sub-domains and the domain.展开更多
基金This work was supported by the Fundamental Research Funds for the Central Universities of Hohai University(Grant No.2019B19414,2019B44914)the Natural Science Foundation of Jiangsu Province for the Youth(Grant No.BK20160853)+2 种基金Key Laboratory of Ministry of Education for Coastal Disaster and Protection,Hohai University(Grant No.202011)the National Natural Science Foundation of China(Grant No.11601151)the National Science Foundation of Zhejiang Province(Grant No.LY19A010003).
文摘In this paper,matrix representations of the best spline quasi-interpolating operator over triangular sub-domains in S_(2)^(1)(△_(mn)^(2),and coefficients of splines in terms of B-net are calculated firstly.Moreover,by means of coefficients in terms of B-net,computation of bivariate numerical cubature over triangular sub-domains with respect to variables x and y is transferred into summation of coefficients of splines in terms of B-net.Thus concise bivariate cubature formulas are constructed over rectangular sub-domain.Furthermore,by means of module of continuity and max-norms,error estimates for cubature formulas are derived over both sub-domains and the domain.
