A LOWER BOUND FOR THE NUMBER OF FUNCTION EVALUATIONS IN AN ERROR ESTIMATE FOR NUMERICAL-INTEGRATION

被引:1
作者
COOLS, R [1 ]
HAEGEMANS, A [1 ]
机构
[1] CATHOLIC UNIV LEUVEN,DEPT COMP SCI,B-3030 HEVERLE,BELGIUM
关键词
Cubature; Error estimate; Lower bound; Quadrature;
D O I
10.1007/BF01888269
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
A popular practical way to estimate the error in numerical integration is to use two cubature formulae. In this paper we give a lower bound for the number of function evaluations necessary to approximate the integral and the error. © 1990 Springer-Verlag New York Inc.
引用
收藏
页码:353 / 361
页数:9
相关论文
共 12 条
[1]   ON THE USE OF GAUSS QUADRATURE IN ADAPTIVE AUTOMATIC INTEGRATION SCHEMES [J].
BERNTSEN, J ;
ESPELID, TO .
BIT, 1984, 24 (02) :239-242
[2]   ON THE CONSTRUCTION OF HIGHER DEGREE 3-DIMENSIONAL EMBEDDED INTEGRATION RULES [J].
BERNTSEN, J ;
ESPELID, TO .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1988, 25 (01) :222-234
[3]   OPTIMAL ADDITION OF KNOTS TO CUBATURE FORMULAS FOR PLANAR REGIONS [J].
COOLS, R ;
HAEGEMANS, A .
NUMERISCHE MATHEMATIK, 1986, 49 (2-3) :269-274
[4]   AN EMBEDDED PAIR OF CUBATURE FORMULAS OF DEGREE-5 AND DEGREE-7 FOR THE TRIANGLE [J].
COOLS, R ;
HAEGEMANS, A .
BIT, 1988, 28 (02) :357-359
[5]   ON THE CONSTRUCTION OF MULTI-DIMENSIONAL EMBEDDED CUBATURE FORMULAS [J].
COOLS, R ;
HAEGEMANS, A .
NUMERISCHE MATHEMATIK, 1989, 55 (06) :735-745
[6]  
COOLS R, 1987, NUMERICAL INTEGRATIO, P165
[7]   AN IMBEDDED FAMILY OF FULLY SYMMETRIC NUMERICAL-INTEGRATION RULES [J].
GENZ, AC ;
MALIK, AA .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1983, 20 (03) :580-588
[8]   PRACTICAL ERROR ESTIMATION IN NUMERICAL-INTEGRATION [J].
LAURIE, DP .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1985, 12-3 (MAY) :425-431
[10]  
MOLLER HM, 1973, THESIS U DORTMUND