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Sibirsk. Mat. Zh., 2016, Volume 57, Number 3, Pages 543–561 (Mi smj2763)  

Optimal cubature formulas for calculation of multidimensional integrals in weighted Sobolev spaces

I. V. Boykov

Penza State University, Penza, Russia

Abstract: Optimal cubature formulas are constructed for calculations of multidimensional integrals in weighted Sobolev spaces. We consider some classes of functions defined in the cube $\Omega=[-1,1]^l$, $l=1,2,…$, and having bounded partial derivatives up to the order $r$ in $\Omega$ and the derivatives of $j$th order ($r<j\le s$) whose modulus tends to infinity as power functions of the form $(d(x,\Gamma))^{-(j-r)}$, where $x\in\Omega\setminus\Gamma$, $x=(x_1,…,x_l)$, $\Gamma=\partial\Omega$, and $d(x,\Gamma)$ is the distance from $x$ to $\Gamma$.

Keywords: weighted Sobolev space, cubature formula, optimal algorithm.

DOI: https://doi.org/10.17377/smzh.2016.57.305

Full text: PDF file (540 kB)
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English version:
Siberian Mathematical Journal, 2016, 57:3, 425–441

Bibliographic databases:

Document Type: Article
UDC: 517.54
Received: 27.10.2014
Revised: 05.10.2015

Citation: I. V. Boykov, “Optimal cubature formulas for calculation of multidimensional integrals in weighted Sobolev spaces”, Sibirsk. Mat. Zh., 57:3 (2016), 543–561; Siberian Math. J., 57:3 (2016), 425–441

Citation in format AMSBIB
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