On passive and active algorithms of reconstruction of functions
We consider passive and active algorithms of reconstruction of functions, satisfying the condition $|f(t′) − f(t″)| ≤ |t′ − t″|^{α},\; 0 < α ≤ 1,$ according to their values $f(t)$ at the points of the interval $[a, b]$. An active algorithm is presented which guarantees, for monotonic function...
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| Date: | 1993 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
1993
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5807 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512030565335040 |
|---|---|
| author | Korneichuk, N. P. Корнейчук, Н. П. Корнейчук, Н. П. |
| author_facet | Korneichuk, N. P. Корнейчук, Н. П. Корнейчук, Н. П. |
| author_sort | Korneichuk, N. P. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:18:17Z |
| description | We consider passive and active algorithms of reconstruction of functions, satisfying the condition $|f(t′) − f(t″)| ≤ |t′ − t″|^{α},\; 0 < α ≤ 1,$ according to their values $f(t)$ at the points of the interval $[a, b]$. An active algorithm is presented which guarantees, for monotonic functions from the above-mentioned class with $0 < α < 1$, a higher order of error in $C [a, b]$ than can be attained by any passive algorithm. |
| first_indexed | 2026-03-24T03:22:18Z |
| format | Article |
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| id | umjimathkievua-article-5807 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:22:18Z |
| publishDate | 1993 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/74/2a5b270e31ce40b933f5666541ec3c74.pdf |
| spelling | umjimathkievua-article-58072020-03-19T09:18:17Z On passive and active algorithms of reconstruction of functions О пассивных и активных алгоритмах восстановления функций Korneichuk, N. P. Корнейчук, Н. П. Корнейчук, Н. П. We consider passive and active algorithms of reconstruction of functions, satisfying the condition $|f(t′) − f(t″)| ≤ |t′ − t″|^{α},\; 0 < α ≤ 1,$ according to their values $f(t)$ at the points of the interval $[a, b]$. An active algorithm is presented which guarantees, for monotonic functions from the above-mentioned class with $0 < α < 1$, a higher order of error in $C [a, b]$ than can be attained by any passive algorithm. Розглядаються пасивні та активні алгоритми відновлення функцій, які задовольняют ь умову $|f(t′) − f(t″)| ≤ |t′ − t″|^{α},\; 0 < α ≤ 1,$ за значеннями $f(t)$ в точках відрізка $[a, b]$. Запропонований активний алгоритм, який при $0 < α < 1$ для монотонних функцій вказаного класу гарантує порядок похибки в $C [a, b]$ більш високий, ніж будь-який пасивний алгоритм. Institute of Mathematics, NAS of Ukraine 1993-02-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5807 Ukrains’kyi Matematychnyi Zhurnal; Vol. 45 No. 2 (1993); 258–264 Український математичний журнал; Том 45 № 2 (1993); 258–264 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5807/8297 https://umj.imath.kiev.ua/index.php/umj/article/view/5807/8298 Copyright (c) 1993 Korneichuk N. P. |
| spellingShingle | Korneichuk, N. P. Корнейчук, Н. П. Корнейчук, Н. П. On passive and active algorithms of reconstruction of functions |
| title | On passive and active algorithms of reconstruction of functions |
| title_alt | О пассивных и активных алгоритмах восстановления функций |
| title_full | On passive and active algorithms of reconstruction of functions |
| title_fullStr | On passive and active algorithms of reconstruction of functions |
| title_full_unstemmed | On passive and active algorithms of reconstruction of functions |
| title_short | On passive and active algorithms of reconstruction of functions |
| title_sort | on passive and active algorithms of reconstruction of functions |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5807 |
| work_keys_str_mv | AT korneichuknp onpassiveandactivealgorithmsofreconstructionoffunctions AT kornejčuknp onpassiveandactivealgorithmsofreconstructionoffunctions AT kornejčuknp onpassiveandactivealgorithmsofreconstructionoffunctions AT korneichuknp opassivnyhiaktivnyhalgoritmahvosstanovleniâfunkcij AT kornejčuknp opassivnyhiaktivnyhalgoritmahvosstanovleniâfunkcij AT kornejčuknp opassivnyhiaktivnyhalgoritmahvosstanovleniâfunkcij |