Approximation of a Multivariate Function of Bounded Variation from its Scattered Data
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2020
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866918256400400384 |
|---|---|
| author | Dachiraju, Rajesh |
| author_facet | Dachiraju, Rajesh |
| contents | This paper addresses the problem of approximating a function of bounded variation from its scattered data. Radial basis function(RBF) interpolation methods are known to approximate only functions in their native spaces, and to date, there has been no known proof that they can approximate functions outside the native space associated with the particular RBF being used. In this paper, we describe a scattered data interpolation method which can approximate any function of bounded variation from its scattered data as the data points grow dense. As the class of functions of bounded variation is a much wider class than the native spaces of the RBF, this method provides a crucial advantage over RBF interpolation methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_11258 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Approximation of a Multivariate Function of Bounded Variation from its Scattered Data Dachiraju, Rajesh Numerical Analysis Analysis of PDEs 42A10 42A15 35C99 This paper addresses the problem of approximating a function of bounded variation from its scattered data. Radial basis function(RBF) interpolation methods are known to approximate only functions in their native spaces, and to date, there has been no known proof that they can approximate functions outside the native space associated with the particular RBF being used. In this paper, we describe a scattered data interpolation method which can approximate any function of bounded variation from its scattered data as the data points grow dense. As the class of functions of bounded variation is a much wider class than the native spaces of the RBF, this method provides a crucial advantage over RBF interpolation methods. |
| title | Approximation of a Multivariate Function of Bounded Variation from its Scattered Data |
| topic | Numerical Analysis Analysis of PDEs 42A10 42A15 35C99 |
| url | https://arxiv.org/abs/2011.11258 |