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Zh. Vychisl. Mat. Mat. Fiz., 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.

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English version:
Computational Mathematics and Mathematical Physics, 2009, 49:1, 1–11

Bibliographic databases:

UDC: 519.644.7
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

Citation in format AMSBIB
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\pages 3--13
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Noskov M.V., Kirillov K.A., “Minimal cubature formulas exact for Haar polynomials”, J. Approx. Theory, 162:3 (2010), 615–627  crossref  mathscinet  zmath  isi  elib  scopus
    2. Kirill A. Kirillov, “Otsenki normy funktsionala pogreshnosti na prostranstvakh $H_\alpha$ kubaturnykh formul, tochnykh dlya polinomov Khaara v dvumernom sluchae”, Zhurn. SFU. Ser. Matem. i fiz., 5:3 (2012), 382–387  mathnet
    3. K. A. Kirillov, “Otsenki na prostranstvakh $S_p$ normy funktsionala pogreshnosti kvadraturnykh formul, tochnykh dlya polinomov Khaara”, Zh. vychisl. matem. i matem. fiz., 52:10 (2012), 1747–1755  mathnet
    4. Kirillov K.A., “Ob otsenkakh pogreshnosti kubaturnykh formul, tochnykh dlya polinomov Khaara”, Vestn. Sibirskogo gos. aerokosmicheskogo un-ta im. akademika M. F. Reshetneva, 2012, no. 2, 33–36  mathscinet  elib
    5. Kirill A. Kirillov, “On Error Estimates for Weighted Quadrature Formulas Exact for Haar Polynomials”, Zhurn. SFU. Ser. Matem. i fiz., 6:3 (2013), 298–307  mathnet
    6. K. A. Kirillov, “Error estimates of cubature formulas exact for Haar polynomials in classes of two-variable functions satisfying a general Lipschitz condition”, Comput. Math. Math. Phys., 53:12 (2013), 1796–1807  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    7. Kirillov K.A., “O tochnykh dlya polinomov Khaara kubaturnykh formulakh ot funktsii dvukh peremennykh, udovletvoryayuschikh obschemu usloviyu Lipshitsa”, Vychislitelnye metody i programmirovanie: novye vychislitelnye tekhnologii, 14:1 (2013), 132–140  mathnet  elib
    8. Kirillov K.A., “Ob otsenke normy funktsionala pogreshnosti na prostranstvakh $S_p$ vesovykh kvadraturnykh formul, tochnykh dlya polinomov Khaara”, Vestnik Krasnoyarskogo gosudarstvennogo agrarnogo universiteta, 2013, no. 7, 30–36  elib
    9. K. A. Kirillov, “Probability error estimates of approximate integration formulas exact for Haar polynomials in $S_p$ classes”, Comput. Math. Math. Phys., 54:11 (2014), 1659–1668  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    10. Kirill A. Kirillov, “On error estimates in $S_p$ for cubature formulas exact for Haar polynomials”, Zhurn. SFU. Ser. Matem. i fiz., 13:4 (2020), 398–413  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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