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Comparison of approximation properties of generalized polynomials and splines

We establish that, for p ∈ [2, ∞), q = 1 or p = ∞, q ∈ [ 1, 2], the classes W p r of functions of many variables defined by restrictions on the L p-norms of mixed derivatives of order r = (r 1, r 2, ..., r m) are better approximated in the L q-metric by periodic generalized splines than by generali...

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Datum:1998
Hauptverfasser: Babenko, V. F., Kofanov, V. A., Pichugov, S. A., Бабенко, В. Ф., Кофанов, В. А., Пичугов, С. А.
Format: Artikel
Sprache:Russisch
Englisch
Veröffentlicht: Institute of Mathematics, NAS of Ukraine 1998
Online Zugang:https://umj.imath.kiev.ua/index.php/umj/article/view/4850
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Назва журналу:Ukrains’kyi Matematychnyi Zhurnal
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Ukrains’kyi Matematychnyi Zhurnal
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author Babenko, V. F.
Kofanov, V. A.
Pichugov, S. A.
Бабенко, В. Ф.
Кофанов, В. А.
Пичугов, С. А.
Бабенко, В. Ф.
Кофанов, В. А.
Пичугов, С. А.
author_facet Babenko, V. F.
Kofanov, V. A.
Pichugov, S. A.
Бабенко, В. Ф.
Кофанов, В. А.
Пичугов, С. А.
Бабенко, В. Ф.
Кофанов, В. А.
Пичугов, С. А.
author_sort Babenko, V. F.
baseUrl_str https://umj.imath.kiev.ua/index.php/umj/oai
collection OJS
datestamp_date 2020-03-18T21:15:53Z
description We establish that, for p ∈ [2, ∞), q = 1 or p = ∞, q ∈ [ 1, 2], the classes W p r of functions of many variables defined by restrictions on the L p-norms of mixed derivatives of order r = (r 1, r 2, ..., r m) are better approximated in the L q-metric by periodic generalized splines than by generalized trigonometric polynomials. In these cases, the best approximations of the Sobolev classes of functions of one variable by trigonometric polynomials and by periodic splines coincide.
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spelling umjimathkievua-article-48502020-03-18T21:15:53Z Comparison of approximation properties of generalized polynomials and splines Сравнение аппроксимационных свойств обобщенных полипомои и сплайнов Babenko, V. F. Kofanov, V. A. Pichugov, S. A. Бабенко, В. Ф. Кофанов, В. А. Пичугов, С. А. Бабенко, В. Ф. Кофанов, В. А. Пичугов, С. А. We establish that, for p ∈ [2, ∞), q = 1 or p = ∞, q ∈ [ 1, 2], the classes W p r of functions of many variables defined by restrictions on the L p-norms of mixed derivatives of order r = (r 1, r 2, ..., r m) are better approximated in the L q-metric by periodic generalized splines than by generalized trigonometric polynomials. In these cases, the best approximations of the Sobolev classes of functions of one variable by trigonometric polynomials and by periodic splines coincide. Встановлено, що класи $W_p^r$ функцій багатьох змінних, які задаються обмеженнями на $L_p$-норми мішаних похідних порядку $r = (r_1, r_2, ..., r_m)$, гірше наближаються в $L_q$-метриці узагальненими тригонометричними поліномами, ніж періодичними узагальненими сплайнами, якщо $p ∈ [2, ∞), q = 1$ або $p = ∞, q ∈ [ 1, 2]$. Найкращі наближення соболєвських класів функцій однієї змінної григономе їричними поліномами і періодичними сплайнами у цих випадках однакові. Institute of Mathematics, NAS of Ukraine 1998-08-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4850 Ukrains’kyi Matematychnyi Zhurnal; Vol. 50 No. 8 (1998); 1011–1020 Український математичний журнал; Том 50 № 8 (1998); 1011–1020 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4850/6399 https://umj.imath.kiev.ua/index.php/umj/article/view/4850/6400 Copyright (c) 1998 Babenko V. F.; Kofanov V. A.; Pichugov S. A.
spellingShingle Babenko, V. F.
Kofanov, V. A.
Pichugov, S. A.
Бабенко, В. Ф.
Кофанов, В. А.
Пичугов, С. А.
Бабенко, В. Ф.
Кофанов, В. А.
Пичугов, С. А.
Comparison of approximation properties of generalized polynomials and splines
title Comparison of approximation properties of generalized polynomials and splines
title_alt Сравнение аппроксимационных свойств обобщенных полипомои и сплайнов
title_full Comparison of approximation properties of generalized polynomials and splines
title_fullStr Comparison of approximation properties of generalized polynomials and splines
title_full_unstemmed Comparison of approximation properties of generalized polynomials and splines
title_short Comparison of approximation properties of generalized polynomials and splines
title_sort comparison of approximation properties of generalized polynomials and splines
url https://umj.imath.kiev.ua/index.php/umj/article/view/4850
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