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This article is cited in 11 scientific papers (total in 11 papers)
Asymptotically sharp bounds for the remainder for the best quadrature formulas for several classes of functions
V. F. Babenko Dnepropetrovsk State University
Abstract:
For certain classes of functions (all functions are defined on a Jordan measurable set $G$) defined by a majorant on the modulus of continuity, we find an asymptotically sharp bound for the remainder of an optimal quadrature formula of the form
$$
\int_Gf(x)\,dx\approx\sum_{\nu=1}^mc_\nu f(x^\nu)
$$
When the given majorant of the modulus of continuity is $t^\alpha$ and the nonnegative function $P(x)$ is such that for any nonnegative numbera the set $\{x\in G:P(x)\le a\}$ is Jordan measurable, then we also find an asymptotically sharp bound for the remainder of an optimal quadrature formula of the form
$$
\int_GP(x)f(x)\,dx\approx\sum_{\nu=1}^mc_\nu f(x^\nu)
$$
Received: 11.12.1974
Citation:
V. F. Babenko, “Asymptotically sharp bounds for the remainder for the best quadrature formulas for several classes of functions”, Mat. Zametki, 19:3 (1976), 313–322; Math. Notes, 19:3 (1976), 187–193
Linking options:
https://www.mathnet.ru/eng/mzm7750 https://www.mathnet.ru/eng/mzm/v19/i3/p313
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Abstract page: | 316 | Full-text PDF : | 134 | First page: | 1 |
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