Geodesic
On a~way of obtaining lower estimates for the errors of quadrature formulas
Sbornik. Mathematics, Tome 71 (1992) no. 1, pp. 247-257

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The purpose of this article is to obtain best possible lower estimates of the errors of quadrature formulas with a fixed number of nodes for classes of functions with bounded mixed derivative. The results obtained here lead to a strengthening of known lower estimates for the deviation of grids. 
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     author = {V. N. Temlyakov},
     title = {On a~way of obtaining lower estimates for the errors of quadrature formulas},
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V. N. Temlyakov. On a~way of obtaining lower estimates for the errors of quadrature formulas. Sbornik. Mathematics, Tome 71 (1992) no. 1, pp. 247-257. http://geodesic.mathdoc.fr/item/SM_1992_71_1_a14/