Gorde:
| Egile nagusia: | |
|---|---|
| Formatua: | Preprint |
| Argitaratua: |
2004
|
| Gaiak: | |
| Sarrera elektronikoa: | https://arxiv.org/abs/math/0403380 |
| Etiketak: |
Etiketa erantsi
Etiketarik gabe, Izan zaitez lehena erregistro honi etiketa jartzen!
|
| _version_ | 1866917022874468352 |
|---|---|
| author | Sablonniere, Paul |
| author_facet | Sablonniere, Paul |
| contents | A new global basis of B-splines is defined in the space of generalized quadratic splines (GQS) generated by Merrien subdivision algorithm. Then, refinement equations for these B-splines and the associated corner-cutting algorithm are given. Afterwards, several applications are presented. First a global construction of monotonic and/or convex generalized splines interpolating monotonic and/or convex data. Second, convergence of sequences of control polygons to the graph of a GQS. Finally, a Lagrange interpolant and a quasi-interpolant which are exact on the space of affine polynomials and whose infinite norms are uniformly bounded independently of the partition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0403380 |
| institution | arXiv |
| publishDate | 2004 |
| record_format | arxiv |
| spellingShingle | Generalized $C^1$ quadratic B-splines generated by Merrien subdivision algorithm and some applications Sablonniere, Paul Numerical Analysis 41A05; 41A35; 65D05; 65D17 A new global basis of B-splines is defined in the space of generalized quadratic splines (GQS) generated by Merrien subdivision algorithm. Then, refinement equations for these B-splines and the associated corner-cutting algorithm are given. Afterwards, several applications are presented. First a global construction of monotonic and/or convex generalized splines interpolating monotonic and/or convex data. Second, convergence of sequences of control polygons to the graph of a GQS. Finally, a Lagrange interpolant and a quasi-interpolant which are exact on the space of affine polynomials and whose infinite norms are uniformly bounded independently of the partition. |
| title | Generalized $C^1$ quadratic B-splines generated by Merrien subdivision algorithm and some applications |
| topic | Numerical Analysis 41A05; 41A35; 65D05; 65D17 |
| url | https://arxiv.org/abs/math/0403380 |