Constructive discretization and approximation in reproducing kernel Hilbert spaces
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866908846360887296 |
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| author | Chkifa, Abdellah Dolbeault, Matthieu Krieg, David Ullrich, Mario |
| author_facet | Chkifa, Abdellah Dolbeault, Matthieu Krieg, David Ullrich, Mario |
| contents | We generalize the sparsification algorithm of Batson, Spielman and Srivastava, making one part of the result dimension-independent. In particular, we recover discretization inequalities in $L_2$- and sup-norms on general finite-dimensional subspaces, prove a suitable infinite-dimensional variant, and discuss the implications for the error of least-squares approximation based on samples. This gives a more constructive version of several recently established approximation bounds, some of which relied on the stronger and less constructive result of Marcus, Spielman and Srivastava. We also improve the constants and oversampling factors in these results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_18719 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Constructive discretization and approximation in reproducing kernel Hilbert spaces Chkifa, Abdellah Dolbeault, Matthieu Krieg, David Ullrich, Mario Numerical Analysis 65D15 We generalize the sparsification algorithm of Batson, Spielman and Srivastava, making one part of the result dimension-independent. In particular, we recover discretization inequalities in $L_2$- and sup-norms on general finite-dimensional subspaces, prove a suitable infinite-dimensional variant, and discuss the implications for the error of least-squares approximation based on samples. This gives a more constructive version of several recently established approximation bounds, some of which relied on the stronger and less constructive result of Marcus, Spielman and Srivastava. We also improve the constants and oversampling factors in these results. |
| title | Constructive discretization and approximation in reproducing kernel Hilbert spaces |
| topic | Numerical Analysis 65D15 |
| url | https://arxiv.org/abs/2602.18719 |