Report
Optimal numerical integration and approximation of functions on $\mathbb{R}^d$ equipped with Gaussian measure
| العنوان: | Optimal numerical integration and approximation of functions on $\mathbb{R}^d$ equipped with Gaussian measure |
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| المؤلفون: | Dũng, Dinh, Nguyen, Van Kien |
| سنة النشر: | 2022 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis |
| الوصف: | We investigate the numerical approximation of integrals over $\mathbb{R}^d$ equipped with the standard Gaussian measure $\gamma$ for integrands belonging to the Gaussian-weighted Sobolev spaces $W^\alpha_p(\mathbb{R}^d, \gamma)$ of mixed smoothness $\alpha \in \mathbb{N}$ for $1 < p < \infty$. We prove the asymptotic order of the convergence of optimal quadratures based on $n$ integration nodes and propose a novel method for constructing asymptotically optimal quadratures. As for related problems, we establish by a similar technique the asymptotic order of the linear, Kolmogorov and sampling $n$-widths in the Gaussian-weighted space $L_q(\mathbb{R}^d, \gamma)$ of the unit ball of $W^\alpha_p(\mathbb{R}^d, \gamma)$ for $1 \leq q < p < \infty$ and $q=p=2$. Comment: 23 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2207.01155 |
| رقم الانضمام: | edsarx.2207.01155 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |