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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2512.19988 |
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| _version_ | 1866912785195073536 |
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| author | Gao, Wenwu Hu, Le Sun, Xingping Zhou, Xuan |
| author_facet | Gao, Wenwu Hu, Le Sun, Xingping Zhou, Xuan |
| contents | We propose and study a general quasi-interpolation framework for stochastic function approximation, which stems and draws motivation from convolution-type solutions for certain practical weighted variational problems.
We obtain our quasi-interpolants using Monte Carlo discretization of the pertinent integrals and establish a family of $L^p$-McDiarmid-type concentration inequalities for $1\leq p\leq \infty$, which resulted in verifiable expected error estimates for the stochastic quasi-interpolants. The $L^1$-version of these concentration inequalities
is dynamically-independent of dimensions, which offers a partial stochastic mitigation of the so called ``curse of dimensionality". The $L^\infty$-version of these concentration inequalities strengthens the existing expected $L^\infty$-error estimates in the literature. Numerical simulation results are provided at the end of the paper to validate the underlying theoretical analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19988 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quasi-interpolation with random sampling centers Gao, Wenwu Hu, Le Sun, Xingping Zhou, Xuan Numerical Analysis We propose and study a general quasi-interpolation framework for stochastic function approximation, which stems and draws motivation from convolution-type solutions for certain practical weighted variational problems. We obtain our quasi-interpolants using Monte Carlo discretization of the pertinent integrals and establish a family of $L^p$-McDiarmid-type concentration inequalities for $1\leq p\leq \infty$, which resulted in verifiable expected error estimates for the stochastic quasi-interpolants. The $L^1$-version of these concentration inequalities is dynamically-independent of dimensions, which offers a partial stochastic mitigation of the so called ``curse of dimensionality". The $L^\infty$-version of these concentration inequalities strengthens the existing expected $L^\infty$-error estimates in the literature. Numerical simulation results are provided at the end of the paper to validate the underlying theoretical analysis. |
| title | Quasi-interpolation with random sampling centers |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2512.19988 |