On the Exact Asymptotics of the Best Relative Approximations of Classes of Periodic Functions by Splines
We obtain the exact asymptotics (as n → ∞) of the best L 1-approximations of classes \(W_1^r\) of periodic functions by splines s ∈ S 2n, r − 1 and s ∈ S 2n, r + k − 1 (S 2n, r is the set of 2π-periodic polynomial splines of order r and defect 1 with nodes at the points kπ/n, k ∈ Z) under certa...
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| Date: | 2001 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
2001
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4270 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1865791388494331904 |
|---|---|
| author | Parfinovych, N. V. Парфинович, Н. В. Парфинович, Н. В. |
| author_facet | Parfinovych, N. V. Парфинович, Н. В. Парфинович, Н. В. |
| author_institution_txt_mv | [
{
"author": "Н. В. Парфинович",
"institution": "Днепропетр. нац. ун-т"
}
] |
| author_sort | Parfinovych, N. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:25:45Z |
| description | We obtain the exact asymptotics (as n → ∞) of the best L 1-approximations of classes \(W_1^r\) of periodic functions by splines s ∈ S 2n, r − 1 and s ∈ S 2n, r + k − 1 (S 2n, r is the set of 2π-periodic polynomial splines of order r and defect 1 with nodes at the points kπ/n, k ∈ Z) under certain restrictions on their derivatives. |
| first_indexed | 2026-03-24T02:56:25Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-4270 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:56:25Z |
| publishDate | 2001 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/f6/2b615b1776ace8d26f7deef6ee07d2f6.pdf |
| spelling | umjimathkievua-article-42702020-03-18T20:25:45Z On the Exact Asymptotics of the Best Relative Approximations of Classes of Periodic Functions by Splines О точных асимптотиках наилучших относительных приближений классов периодических функций сплайнами Parfinovych, N. V. Парфинович, Н. В. Парфинович, Н. В. We obtain the exact asymptotics (as n → ∞) of the best L 1-approximations of classes \(W_1^r\) of periodic functions by splines s ∈ S 2n, r − 1 and s ∈ S 2n, r + k − 1 (S 2n, r is the set of 2π-periodic polynomial splines of order r and defect 1 with nodes at the points kπ/n, k ∈ Z) under certain restrictions on their derivatives. Знайдено точну асимптотику (при $n → ∞$) найкращих $L_1$-наближень класів $W_1^r$ періодичних функцій сплайнами $s ∈ S_{2n, r − 1}$ та $s ∈ S_{2n, r + k − 1}$, ($S_{2n, r}$ — множина $2π$-періодичних поліноміальних сплайнів порядку $r $, дефекту 1 з вузлами в точках $kπ/n,\; k ∈ Z$) з обмеженнями на їх похідні. Institute of Mathematics, NAS of Ukraine 2001-04-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4270 Ukrains’kyi Matematychnyi Zhurnal; Vol. 53 No. 4 (2001); 489-500 Український математичний журнал; Том 53 № 4 (2001); 489-500 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4270/5244 https://umj.imath.kiev.ua/index.php/umj/article/view/4270/5245 Copyright (c) 2001 Parfinovych N. V. |
| spellingShingle | Parfinovych, N. V. Парфинович, Н. В. Парфинович, Н. В. On the Exact Asymptotics of the Best Relative Approximations of Classes of Periodic Functions by Splines |
| title | On the Exact Asymptotics of the Best Relative Approximations of Classes of Periodic Functions by Splines |
| title_alt | О точных асимптотиках наилучших относительных приближений
классов периодических функций сплайнами |
| title_full | On the Exact Asymptotics of the Best Relative Approximations of Classes of Periodic Functions by Splines |
| title_fullStr | On the Exact Asymptotics of the Best Relative Approximations of Classes of Periodic Functions by Splines |
| title_full_unstemmed | On the Exact Asymptotics of the Best Relative Approximations of Classes of Periodic Functions by Splines |
| title_short | On the Exact Asymptotics of the Best Relative Approximations of Classes of Periodic Functions by Splines |
| title_sort | on the exact asymptotics of the best relative approximations of classes of periodic functions by splines |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4270 |
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