On geometric interpolation by planar parametric polynomial curves
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- by Gašper Jaklič, Jernej Kozak, Marjeta Krajnc and Emil Žagar PDF
- Math. Comp. 76 (2007), 1981-1993 Request permission
Abstract:
In this paper the problem of geometric interpolation of planar data by parametric polynomial curves is revisited. The conjecture that a parametric polynomial curve of degree $\le n$ can interpolate $2 n$ given points in $\mathbb {R}^2$ is confirmed for $n \le 5$ under certain natural restrictions. This conclusion also implies the optimal asymptotic approximation order. More generally, the optimal order $2 n$ can be achieved as soon as the interpolating curve exists.References
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Additional Information
- Gašper Jaklič
- Affiliation: Institute of Mathematics, Physics and Mechanics, Jadranska 19, SI-1000 Ljubljana, Slovenia
- Email: gasper.jaklic@fmf.uni-lj.si
- Jernej Kozak
- Affiliation: Department of Mathematics and Institute of Mathematics, Physics and Mechanics, Jadranska 19, SI-1000 Ljubljana, Slovenia
- Email: jernej.kozak@fmf.uni-lj.si
- Marjeta Krajnc
- Affiliation: Institute of Mathematics, Physics and Mechanics, Jadranska 19, SI-1000 Ljubljana, Slovenia
- Email: marjetka.krajnc@fmf.uni-lj.si
- Emil Žagar
- Affiliation: Department of Mathematics and Institute of Mathematics, Physics and Mechanics, Jadranska 19, SI-1000 Ljubljana, Slovenia
- Email: emil.zagar@fmf.uni-lj.si
- Received by editor(s): September 4, 2006
- Received by editor(s) in revised form: September 7, 2006
- Published electronically: May 9, 2007
- Additional Notes: The second and fourth authors were partially supported by Ministry of Higher Education, Science and Technology of Slovenia
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 76 (2007), 1981-1993
- MSC (2000): Primary 41A05, 41A10, 41A25, 65D05, 65D17; Secondary 65D10
- DOI: https://doi.org/10.1090/S0025-5718-07-01988-6
- MathSciNet review: 2336277