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 |
| Published: |
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 |
| Summary: | 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. |
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| ISSN: | 1029-242X |