Laguerre- and Laplace-weighted integration of mixed-smoothness functions
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908731748384768 |
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| author | Dũng, Dinh |
| author_facet | Dũng, Dinh |
| contents | We investigate the approximation of generalized Laguerre- or Laplace-weighted integrals over $\mathbb{R}^d_+$ or $\mathbb{R}^d$ of functions from generalized Laguerre- or Laplace-weighted Sobolev spaces of mixed smoothness, respectively. We prove upper and lower bounds of the convergence rate of optimal quadratures with respect to $n$ integration nodes for functions from these spaces. The upper bound is performed by sparse-grid quadratures with integration nodes on step hyperbolic corners or hyperbolic crosses in the function domain $\mathbb{R}^d_+$ or $\mathbb{R}^d$, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21489 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Laguerre- and Laplace-weighted integration of mixed-smoothness functions Dũng, Dinh Numerical Analysis We investigate the approximation of generalized Laguerre- or Laplace-weighted integrals over $\mathbb{R}^d_+$ or $\mathbb{R}^d$ of functions from generalized Laguerre- or Laplace-weighted Sobolev spaces of mixed smoothness, respectively. We prove upper and lower bounds of the convergence rate of optimal quadratures with respect to $n$ integration nodes for functions from these spaces. The upper bound is performed by sparse-grid quadratures with integration nodes on step hyperbolic corners or hyperbolic crosses in the function domain $\mathbb{R}^d_+$ or $\mathbb{R}^d$, respectively. |
| title | Laguerre- and Laplace-weighted integration of mixed-smoothness functions |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2512.21489 |