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Mat. Zametki, 2017, Volume 101, Issue 2, Pages 262–285 (Mi mz11002)  

Mean Oscillation Modulus and Number-Theoretic Grid Quadrature Formulas

E. A. Sevast'yanov

National Engineering Physics Institute "MEPhI", Moscow

Abstract: For arbitrary Riemann integrable functions $f$ and irrational numbers $\theta \in (0,1)$, we obtain estimates of the error $R_n(f,\theta)$ of the quadrature formula
$$ \int_{0}^{1}f(x) dx=\frac{1}{n}\sum_{k=1}^nf(\{k\theta\})- R_n(f,\theta) $$
in which $\{k\theta\}$ is the fractional part of the number $k\theta$.

Keywords: quadrature formula, continued fraction, type of an irrational number, mean oscillation modulus.

DOI: https://doi.org/10.4213/mzm11002

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English version:
Mathematical Notes, 2017, 101:2, 320–340

Bibliographic databases:

UDC: 511+511.9
Received: 15.10.2015

Citation: E. A. Sevast'yanov, “Mean Oscillation Modulus and Number-Theoretic Grid Quadrature Formulas”, Mat. Zametki, 101:2 (2017), 262–285; Math. Notes, 101:2 (2017), 320–340

Citation in format AMSBIB
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