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A lower bound for the error of a formula for approximate summation in the class Es,p(C)

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Abstract

The error of a formula for approximate summation in the class ES,P(C) over an arbitrary mesh containing p base-points is shown to be not less than C1 1nsp/p. This estimate has the same order as the error of the optimal parallelepiped mesh in this class.

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Literature cited

  1. N. M. Korobov, “On some problems in theory of Diophantine approximations,” Usp. Mat. Nauk,22, No. 3, 83–118 (1967).

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  2. I. F. Sharygin, “On the application of number-theoretic methods of approximate integration in the case of nonperiodic functions,” Dokl. Akad. Nauk SSSR,132, No. 1, 71–74 (1960).

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Authors and Affiliations

  1. Institute of Control, Moscow

    I. F. Sharygin

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  1. I. F. Sharygin
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Translated from Matematicheskie Zametki, Vol. 21, No. 3, pp. 371–375, March, 1977.

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Sharygin, I.F. A lower bound for the error of a formula for approximate summation in the class Es,p(C). Mathematical Notes of the Academy of Sciences of the USSR 21, 207–210 (1977). https://doi.org/10.1007/BF01106745

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  • DOI: https://doi.org/10.1007/BF01106745

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