Scattered Data Histopolation in Averaging Kernel Hilbert Spaces
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909988531732480 |
|---|---|
| author | Bruno, Ludovico Bruni Cappellazzo, Giacomo Erb, Wolfgang Esfahani, Mohammad Karimnejad |
| author_facet | Bruno, Ludovico Bruni Cappellazzo, Giacomo Erb, Wolfgang Esfahani, Mohammad Karimnejad |
| contents | Kernel-based methods offer a powerful and flexible mathematical framework for addressing histopolation problems. In histopolation, the available input data does not consist of pointwise function samples but of averages taken over intervals or higher-dimensional regions, and these mean values serve as a basis for reconstructing or approximating the target function. While classical interpolation requires continuity of the underlying function, histopolation can be performed in larger function spaces. In the framework of kernel methods, we will introduce and study the so-called averaging kernel Hilbert spaces (AKHS's) for this purpose. Within this setting, we develop systematic construction principles for averaging kernels and provide characterizations based on the Fourier-Plancherel transform. In addition, we analyze several representative histopolation scenarios in order to highlight properties of this approximation method, including conditions for unisolvence and possible error estimates. Finally, we present numerical experiments that shed some light on the convergence behavior of the presented approach and demonstrate its practical effectiveness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07967 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Scattered Data Histopolation in Averaging Kernel Hilbert Spaces Bruno, Ludovico Bruni Cappellazzo, Giacomo Erb, Wolfgang Esfahani, Mohammad Karimnejad Numerical Analysis 41A05, 46E22, 65D12 Kernel-based methods offer a powerful and flexible mathematical framework for addressing histopolation problems. In histopolation, the available input data does not consist of pointwise function samples but of averages taken over intervals or higher-dimensional regions, and these mean values serve as a basis for reconstructing or approximating the target function. While classical interpolation requires continuity of the underlying function, histopolation can be performed in larger function spaces. In the framework of kernel methods, we will introduce and study the so-called averaging kernel Hilbert spaces (AKHS's) for this purpose. Within this setting, we develop systematic construction principles for averaging kernels and provide characterizations based on the Fourier-Plancherel transform. In addition, we analyze several representative histopolation scenarios in order to highlight properties of this approximation method, including conditions for unisolvence and possible error estimates. Finally, we present numerical experiments that shed some light on the convergence behavior of the presented approach and demonstrate its practical effectiveness. |
| title | Scattered Data Histopolation in Averaging Kernel Hilbert Spaces |
| topic | Numerical Analysis 41A05, 46E22, 65D12 |
| url | https://arxiv.org/abs/2601.07967 |