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. 
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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/

[1] Turetskii A. Kh., “Ob otsenkakh priblizhenii kvadraturnymi formulami dlya funktsii, udovletvoryayuschikh usloviyu Lipshitsa”, UMN, 6:5(45) (1951), 166–171 | MR

[2] Nikolskii S. M., Kvadraturnye formuly, Izd. 3-e s dobavleniem N. P. Korneichuka, Nauka, M., 1979 | MR