Gel’fand-N-width in probabilistic setting
Abstract In this article, we first put forward a new definition of probabilistic Gel’fand- ( N , δ ) $(N,\delta )$ -width which is the classical Gel’fand-N-width in a probabilistic setting. Then we estimate the sharp order of the probabilistic Gel’fand- ( N , δ ) $(N,\delta )$ -width of finite-dimen...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-05-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-020-02409-6 |
| _version_ | 1818173823339462656 |
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| author | Xin Tan Yanan Wang Lu Sun Xingfeng Shao Guanggui Chen |
| author_facet | Xin Tan Yanan Wang Lu Sun Xingfeng Shao Guanggui Chen |
| author_sort | Xin Tan |
| collection | DOAJ |
| description | Abstract In this article, we first put forward a new definition of probabilistic Gel’fand- ( N , δ ) $(N,\delta )$ -width which is the classical Gel’fand-N-width in a probabilistic setting. Then we estimate the sharp order of the probabilistic Gel’fand- ( N , δ ) $(N,\delta )$ -width of finite-dimensional space. Furthermore, we obtain the exact order of probabilistic Gel’fand- ( N , δ ) $(N, \delta )$ -width of univariate Sobolev space by the discretization method according to the result of finite-dimensional space. |
| first_indexed | 2024-12-11T19:34:38Z |
| format | Article |
| id | doaj.art-0ace9c7cc11440e0adeec79826f3e962 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-11T19:34:38Z |
| publishDate | 2020-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-0ace9c7cc11440e0adeec79826f3e9622022-12-22T00:53:11ZengSpringerOpenJournal of Inequalities and Applications1029-242X2020-05-012020111410.1186/s13660-020-02409-6Gel’fand-N-width in probabilistic settingXin Tan0Yanan Wang1Lu Sun2Xingfeng Shao3Guanggui Chen4School of Science, Xihua UniversitySchool of Science, Xihua UniversitySchool of Science, Xihua UniversitySchool of Science, Xihua UniversityGraduate Department, Xihua UniversityAbstract In this article, we first put forward a new definition of probabilistic Gel’fand- ( N , δ ) $(N,\delta )$ -width which is the classical Gel’fand-N-width in a probabilistic setting. Then we estimate the sharp order of the probabilistic Gel’fand- ( N , δ ) $(N,\delta )$ -width of finite-dimensional space. Furthermore, we obtain the exact order of probabilistic Gel’fand- ( N , δ ) $(N, \delta )$ -width of univariate Sobolev space by the discretization method according to the result of finite-dimensional space.http://link.springer.com/article/10.1186/s13660-020-02409-6Probabilistic Gel’fand- ( N , δ ) $(N,\delta )$ -widthFinite-dimensional spaceUnivariate Sobolev space |
| spellingShingle | Xin Tan Yanan Wang Lu Sun Xingfeng Shao Guanggui Chen Gel’fand-N-width in probabilistic setting Journal of Inequalities and Applications Probabilistic Gel’fand- ( N , δ ) $(N,\delta )$ -width Finite-dimensional space Univariate Sobolev space |
| title | Gel’fand-N-width in probabilistic setting |
| title_full | Gel’fand-N-width in probabilistic setting |
| title_fullStr | Gel’fand-N-width in probabilistic setting |
| title_full_unstemmed | Gel’fand-N-width in probabilistic setting |
| title_short | Gel’fand-N-width in probabilistic setting |
| title_sort | gel fand n width in probabilistic setting |
| topic | Probabilistic Gel’fand- ( N , δ ) $(N,\delta )$ -width Finite-dimensional space Univariate Sobolev space |
| url | http://link.springer.com/article/10.1186/s13660-020-02409-6 |
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