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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

On geometric interpolation by planar parametric polynomial curves


Authors: Gasper Jaklic, Jernej Kozak, Marjeta Krajnc and Emil Zagar
Journal: Math. Comp. 76 (2007), 1981-1993
MSC (2000): Primary 41A05, 41A10, 41A25, 65D05, 65D17, \linebreak; Secondary 65D10
Published electronically: May 9, 2007
MathSciNet review: 2336277
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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.


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Additional Information

Gasper Jaklic
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 Zagar
Affiliation: Department of Mathematics and Institute of Mathematics, Physics and Mechanics, Jadranska 19, SI-1000 Ljubljana, Slovenia
Email: emil.zagar@fmf.uni-lj.si

DOI: http://dx.doi.org/10.1090/S0025-5718-07-01988-6
PII: S 0025-5718(07)01988-6
Keywords: Geometric interpolation, approximation order, asymptotic analysis
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
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.