Nonlinear stationary subdivision schemes that reproduce trigonometric functions
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arXiv
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| Format: | Preprint |
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2018
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| _version_ | 1866913592401461248 |
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| author | Donat, Rosa López-Ureña, Sergio |
| author_facet | Donat, Rosa López-Ureña, Sergio |
| contents | In this paper we define a family of nonlinear, stationary, interpolatory subdivision schemes with the capability of reproducing conic shapes including polynomials upto second order. Linear, non-stationary, subdivision schemes do also achieve this goal, but different conic sections require different refinement rules to guarantee exact reproduction. On the other hand, with our construction, exact reproduction of different conic shapes can be achieved using exactly the same nonlinear scheme. Convergence, stability, approximation and shape preservation properties of the new schemes are analyzed. In addition, the conditions to obtain $\mathcal{C}^1$ limit functions are also studied. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1809_03731 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Nonlinear stationary subdivision schemes that reproduce trigonometric functions Donat, Rosa López-Ureña, Sergio Numerical Analysis 41A25, 41A30, 65D15, 65D17 In this paper we define a family of nonlinear, stationary, interpolatory subdivision schemes with the capability of reproducing conic shapes including polynomials upto second order. Linear, non-stationary, subdivision schemes do also achieve this goal, but different conic sections require different refinement rules to guarantee exact reproduction. On the other hand, with our construction, exact reproduction of different conic shapes can be achieved using exactly the same nonlinear scheme. Convergence, stability, approximation and shape preservation properties of the new schemes are analyzed. In addition, the conditions to obtain $\mathcal{C}^1$ limit functions are also studied. |
| title | Nonlinear stationary subdivision schemes that reproduce trigonometric functions |
| topic | Numerical Analysis 41A25, 41A30, 65D15, 65D17 |
| url | https://arxiv.org/abs/1809.03731 |