Geodesic
Optimal error of numerical integration with regard to function values at integration points
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 10 (2007) no. 1, pp. 29-42

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In the paper, we consider a corrected definition for the numerical integration error norm with regard to function values at integration points. Optimal and suboptimal integration formulas are obtained for different functional spaces. 
@article{SJVM_2007_10_1_a1,
     author = {N. K. Bakirov},
     title = {Optimal error of numerical integration with regard to function values at integration points},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {29--42},
     publisher = {mathdoc},
     volume = {10},
     number = {1},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2007_10_1_a1/}
}
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N. K. Bakirov. Optimal error of numerical integration with regard to function values at integration points. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 10 (2007) no. 1, pp. 29-42. http://geodesic.mathdoc.fr/item/SJVM_2007_10_1_a1/