|
Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2009, Volume 49, Number 1, Pages 3–13
(Mi zvmmf49)
|
|
|
|
This article is cited in 10 scientific papers (total in 10 papers)
Error estimates in $S_p$ for cubature formulas exact for Haar polynomials in the two-dimensional case
K. A. Kirillov, M. V. Noskov Siberian Federal University, ul. Kirenskogo 26, Krasnoyarsk, 660074, Russia
Abstract:
On the spaces $S_p$, an upper estimate is found for the norm of the error functional $\delta_N(f)$ of cubature formulas possessing the Haar $d$-property in the two-dimensional case. An asymptotic relation is proved for $\|\delta_N(f)\|_{S_p^*}$ with the number of nodes $N\sim 2^d$, where $d\to\infty$. For $N\sim 2^d$ with $d\to\infty$, it is shown that the norm of $\delta_N$ for the formulas under study has the best convergence rate, which is equal to $N^{-1/p}$.
Key words:
cubature formulas in the space of Haar functions, error estimates for cubature formulas, estimate for the best convergence rate.
Received: 10.04.2008
Citation:
K. A. Kirillov, M. V. Noskov, “Error estimates in $S_p$ for cubature formulas exact for Haar polynomials in the two-dimensional case”, Zh. Vychisl. Mat. Mat. Fiz., 49:1 (2009), 3–13; Comput. Math. Math. Phys., 49:1 (2009), 1–11
Linking options:
https://www.mathnet.ru/eng/zvmmf49 https://www.mathnet.ru/eng/zvmmf/v49/i1/p3
|
Statistics & downloads: |
Abstract page: | 340 | Full-text PDF : | 91 | References: | 40 | First page: | 9 |
|