In this paper,matrix representations of the best spline quasi-interpolating operator over triangular sub-domains in S12(Δ(2)mn),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.

Jiang Qian;Xiquan Shi;Jinming Wu;Dianxuan Gong

College of Science,Hohai University,Nanjing 211100,China;Key Laboratory of Coastal Disaster and Defence(Hohai University),Ministry of Education,Nanjing 210098,China;Division of Physics,Engineering,Mathematics,and Computer Science,Delaware State University,Dover,DE 19901,USA;Statistics and Mathematics Institute,Zhejiang Gongshang University,Hangzhou 310018,China;College of Science,North China University of Science and Technology,Tangshan 063210,China

计算数学（英文版）

[1]Jiang Qian;Xiquan Shi;Jinming Wu;Dianxuan Gong-.CONSTRUCTION OF CUBATURE FORMULAS VIA BIVARIATE QUADRATIC SPLINE SPACES OVER NON-UNIFORM TYPE-2 TRIANGULATION)[J].计算数学（英文版）,2022(02):205-230

CONSTRUCTION,CUBATURE,BIVARIATE,QUADRATIC,SPLINE,SPACES,UNIFORM,TRIANGULATION

OF,FORMULAS,VIA,OVER,NON,TYPE,In,this,paper,matrix,representations,best,quasi,interpolating,operator,triangular,sub,domains,S12,mn,coefficients,splines,terms,net,are,calculated,firstly,Moreover,by,means,computation,bivariate,numerical,cubature,respect,variables,transferred,into,summation,Thus,concise,formulas,constructed,rectangular,Furthermore,module,continuity,max,norms,error,estimates,derived,both

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