Box-splines orthogonal projections
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2018
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909447201226752 |
|---|---|
| author | Beśka, M. Dziedziul, K. |
| author_facet | Beśka, M. Dziedziul, K. |
| contents | Let $P$ be orthogonal projection on B-splines of degree $r-1$ with equally spaced knots. Sweldens and Piessens proved that $P(x^r)-x^r$ is Bernoulli polynomial. We generalize Sweldens ans Piessens's result for box-splines. It gives the opportunity to define the seminorm of Sobolev space in terms of the asymptotic formula for the error in orthogonal projection. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1812_01700 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Box-splines orthogonal projections Beśka, M. Dziedziul, K. Classical Analysis and ODEs Let $P$ be orthogonal projection on B-splines of degree $r-1$ with equally spaced knots. Sweldens and Piessens proved that $P(x^r)-x^r$ is Bernoulli polynomial. We generalize Sweldens ans Piessens's result for box-splines. It gives the opportunity to define the seminorm of Sobolev space in terms of the asymptotic formula for the error in orthogonal projection. |
| title | Box-splines orthogonal projections |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/1812.01700 |