Optimal Subspaces for Mean Square Approximation of Classes of Differentiable Functions on a Segment

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Optimal Subspaces for Mean Square Approximation of Classes of Differentiable Functions on a Segment. / Vinogradov, O. L.; Ulitskaya, A. Yu.

в: Vestnik St. Petersburg University: Mathematics, Том 53, № 3, 01.07.2020, стр. 270-281.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{dc2ffe0b27f44e09a7893f857e75522e,

title = "Optimal Subspaces for Mean Square Approximation of Classes of Differentiable Functions on a Segment",

abstract = "In this paper, a set of optimal subspaces is specified for L-2 approximation of three classes of functions in the Sobolev spaces W-2((r)) defined on a segment and subject to certain boundary conditions. A subspaceXof a dimension not exceedingnis called optimal for a function class A if the best approximation of A by X is equal to the Kolmogorovn-width of A. These boundary conditions correspond to subspaces of periodically extended functions with symmetry properties. All approximating subspaces are generated by equidistant shifts of a single function. The conditions of optimality are given in terms of Fourier coefficients of a generating function. In particular, we indicate optimal spline spaces of all degrees d greater than or similar to r-1 with equidistant knots of several different types.",

keywords = "n-widths, spaces of shifts, splines",

author = "Vinogradov, {O. L.} and Ulitskaya, {A. Yu}",

note = "Funding Information: This work is supported by the Russian Science Foundation under grant no. 18-11-00055. Publisher Copyright: {\textcopyright} 2020, Pleiades Publishing, Ltd. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",

year = "2020",

month = jul,

day = "1",

doi = "10.1134/S1063454120030164",

language = "English",

volume = "53",

pages = "270--281",

journal = "Vestnik St. Petersburg University: Mathematics",

issn = "1063-4541",

publisher = "Pleiades Publishing",

number = "3",

}

RIS

TY - JOUR

T1 - Optimal Subspaces for Mean Square Approximation of Classes of Differentiable Functions on a Segment

AU - Vinogradov, O. L.

AU - Ulitskaya, A. Yu

N1 - Funding Information: This work is supported by the Russian Science Foundation under grant no. 18-11-00055. Publisher Copyright: © 2020, Pleiades Publishing, Ltd. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/7/1

Y1 - 2020/7/1

N2 - In this paper, a set of optimal subspaces is specified for L-2 approximation of three classes of functions in the Sobolev spaces W-2((r)) defined on a segment and subject to certain boundary conditions. A subspaceXof a dimension not exceedingnis called optimal for a function class A if the best approximation of A by X is equal to the Kolmogorovn-width of A. These boundary conditions correspond to subspaces of periodically extended functions with symmetry properties. All approximating subspaces are generated by equidistant shifts of a single function. The conditions of optimality are given in terms of Fourier coefficients of a generating function. In particular, we indicate optimal spline spaces of all degrees d greater than or similar to r-1 with equidistant knots of several different types.

AB - In this paper, a set of optimal subspaces is specified for L-2 approximation of three classes of functions in the Sobolev spaces W-2((r)) defined on a segment and subject to certain boundary conditions. A subspaceXof a dimension not exceedingnis called optimal for a function class A if the best approximation of A by X is equal to the Kolmogorovn-width of A. These boundary conditions correspond to subspaces of periodically extended functions with symmetry properties. All approximating subspaces are generated by equidistant shifts of a single function. The conditions of optimality are given in terms of Fourier coefficients of a generating function. In particular, we indicate optimal spline spaces of all degrees d greater than or similar to r-1 with equidistant knots of several different types.

KW - n-widths

KW - spaces of shifts

KW - splines

UR - http://www.scopus.com/inward/record.url?scp=85090048492&partnerID=8YFLogxK

U2 - 10.1134/S1063454120030164

DO - 10.1134/S1063454120030164

M3 - Article

AN - SCOPUS:85090048492

VL - 53

SP - 270

EP - 281

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 3

ER -

ID: 72082167