On approximation of functions from below by splines of the best approximation with free nodes
Let M be the set of functions integrable to the power β=(r+1+1/p)-1. We obtain asymptotically exact lower bounds for the approximation of individual functions from the set M by splines of the best approximation of degree rand defect k in the metric of L p.
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| Дата: | 2000 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Російська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2000
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/4440 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510570459955200 |
|---|---|
| author | Shumeiko, A. A. Шумейко, А. А. Шумейко, А. А. |
| author_facet | Shumeiko, A. A. Шумейко, А. А. Шумейко, А. А. |
| author_sort | Shumeiko, A. A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:29:03Z |
| description | Let M be the set of functions integrable to the power β=(r+1+1/p)-1. We obtain asymptotically exact lower bounds for the approximation of individual functions from the set M by splines of the best approximation of degree rand defect k in the metric of L p. |
| first_indexed | 2026-03-24T02:59:06Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-4440 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:59:06Z |
| publishDate | 2000 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/db/a2265b419b2975337c71fe9e003545db.pdf |
| spelling | umjimathkievua-article-44402020-03-18T20:29:03Z On approximation of functions from below by splines of the best approximation with free nodes О приближении снизу функций сплайнами наилучшего приближения со свободными узлами Shumeiko, A. A. Шумейко, А. А. Шумейко, А. А. Let M be the set of functions integrable to the power β=(r+1+1/p)-1. We obtain asymptotically exact lower bounds for the approximation of individual functions from the set M by splines of the best approximation of degree rand defect k in the metric of L p. Нехай — деяка множина функцій таких, що інтеграл від функції в степені $β=(r+1+1/p)^{-1}$ збігається. Отримано асимптотично точні оцінки знизу наближення індивідуальних функцій із множини $M$ сплайнами найкращого наближення степеня $r$ дефекіу $k$ в метриці $L_p$ Institute of Mathematics, NAS of Ukraine 2000-04-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4440 Ukrains’kyi Matematychnyi Zhurnal; Vol. 52 No. 4 (2000); 512-523 Український математичний журнал; Том 52 № 4 (2000); 512-523 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4440/5584 https://umj.imath.kiev.ua/index.php/umj/article/view/4440/5585 Copyright (c) 2000 Shumeiko A. A. |
| spellingShingle | Shumeiko, A. A. Шумейко, А. А. Шумейко, А. А. On approximation of functions from below by splines of the best approximation with free nodes |
| title | On approximation of functions from below by splines of the best approximation with free nodes |
| title_alt | О приближении снизу функций сплайнами наилучшего приближения со свободными узлами |
| title_full | On approximation of functions from below by splines of the best approximation with free nodes |
| title_fullStr | On approximation of functions from below by splines of the best approximation with free nodes |
| title_full_unstemmed | On approximation of functions from below by splines of the best approximation with free nodes |
| title_short | On approximation of functions from below by splines of the best approximation with free nodes |
| title_sort | on approximation of functions from below by splines of the best approximation with free nodes |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4440 |
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