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numerical analysis
This paper is concerned with minimizing the norm of the remainder of integration formula. The author states that for some classes of functions the minimum is achieved only if the remainder vanishes for every polynomial of degree $< r$.
[1] В. И. Крылов: Приближенное вычисление интегралов. Москва 1959. Zbl 1047.90504
[2] С. M. Никольский: Квадратурные формулы. Москва 1958. Zbl 0995.62501
[3] A. Sard: Best approximate integration formulas. Best approximation formulas. American Journal of Math. 71, 1949, 80-91. DOI 10.2307/2372095 | MR 0029283 | Zbl 0039.34104
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