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Spherical cubature formulas in Sobolev spaces. / Vaskevich, V. L.

In: Siberian Mathematical Journal, Vol. 58, No. 3, 01.05.2017, p. 408-418.

Research output: Contribution to journal › Article › peer-review

Harvard

Vaskevich, VL 2017, 'Spherical cubature formulas in Sobolev spaces', Siberian Mathematical Journal, vol. 58, no. 3, pp. 408-418. https://doi.org/10.1134/S0037446617030053

APA

Vaskevich, V. L. (2017). Spherical cubature formulas in Sobolev spaces. Siberian Mathematical Journal, 58(3), 408-418. https://doi.org/10.1134/S0037446617030053

Vancouver

Vaskevich VL. Spherical cubature formulas in Sobolev spaces. Siberian Mathematical Journal. 2017 May 1;58(3):408-418. doi: 10.1134/S0037446617030053

Author

Vaskevich, V. L. / Spherical cubature formulas in Sobolev spaces. In: Siberian Mathematical Journal. 2017 ; Vol. 58, No. 3. pp. 408-418.

BibTeX

@article{bb3fc9eac035410e8b1fb693994ac0c4,
title = "Spherical cubature formulas in Sobolev spaces",
abstract = "We study sequences of cubature formulas on the unit sphere in a multidimensional Euclidean space. The grids for the cubature formulas under consideration embed in each other consecutively, forming in the limit a dense subset on the initial sphere. As the domain of cubature formulas, i.e. as the class of integrands, we take spherical Sobolev spaces. These spaces may have fractional smoothness. We prove that, among all possible spherical cubature formulas with given grid, there exists and is unique a formula with the least norm of the error, an optimal formula. The weights of the optimal cubature formula are shown to be solutions to a special nondegenerate system of linear equations. We prove that the errors of cubature formulas tend to zero as the number of nodes grows indefinitely.",
keywords = "embedding constant, embedding function, error, optimal formula, Sobolev-like space on a multidimensional sphere, spherical cubature formula",
author = "Vaskevich, {V. L.}",
year = "2017",
month = may,
day = "1",
doi = "10.1134/S0037446617030053",
language = "English",
volume = "58",
pages = "408--418",
journal = "Siberian Mathematical Journal",
issn = "0037-4466",
publisher = "MAIK NAUKA/INTERPERIODICA/SPRINGER",
number = "3",

}

RIS

TY - JOUR

T1 - Spherical cubature formulas in Sobolev spaces

AU - Vaskevich, V. L.

PY - 2017/5/1

Y1 - 2017/5/1

N2 - We study sequences of cubature formulas on the unit sphere in a multidimensional Euclidean space. The grids for the cubature formulas under consideration embed in each other consecutively, forming in the limit a dense subset on the initial sphere. As the domain of cubature formulas, i.e. as the class of integrands, we take spherical Sobolev spaces. These spaces may have fractional smoothness. We prove that, among all possible spherical cubature formulas with given grid, there exists and is unique a formula with the least norm of the error, an optimal formula. The weights of the optimal cubature formula are shown to be solutions to a special nondegenerate system of linear equations. We prove that the errors of cubature formulas tend to zero as the number of nodes grows indefinitely.

AB - We study sequences of cubature formulas on the unit sphere in a multidimensional Euclidean space. The grids for the cubature formulas under consideration embed in each other consecutively, forming in the limit a dense subset on the initial sphere. As the domain of cubature formulas, i.e. as the class of integrands, we take spherical Sobolev spaces. These spaces may have fractional smoothness. We prove that, among all possible spherical cubature formulas with given grid, there exists and is unique a formula with the least norm of the error, an optimal formula. The weights of the optimal cubature formula are shown to be solutions to a special nondegenerate system of linear equations. We prove that the errors of cubature formulas tend to zero as the number of nodes grows indefinitely.

KW - embedding constant

KW - embedding function

KW - error

KW - optimal formula

KW - Sobolev-like space on a multidimensional sphere

KW - spherical cubature formula

UR - http://www.scopus.com/inward/record.url?scp=85021270116&partnerID=8YFLogxK

U2 - 10.1134/S0037446617030053

DO - 10.1134/S0037446617030053

M3 - Article

AN - SCOPUS:85021270116

VL - 58

SP - 408

EP - 418

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 3

ER -

ID: 10183120