On planar polynomial geometric interpolation

In the paper, the planar polynomial geometric interpolation of data points is revisited. Simple sufficient geometric conditions that imply the existence of the interpolant are derived in general. They require data points to be convex in a certain discrete sense. Since the geometric interpolation is...

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Bibliographic Details
Published in:Journal of approximation theory Vol. 283; p. 105806
Main Author: Kozak, Jernej
Format: Journal Article
Language:English
Published: Elsevier Inc 01.11.2022
Subjects:
Approximation order
Existence
Geometric interpolation
Polynomial curve
Geometric interpolation
Approximation order
41A10
Polynomial curve
65D05
65D17
Existence
ISSN:0021-9045, 1096-0430
Online Access:Get full text
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Summary:In the paper, the planar polynomial geometric interpolation of data points is revisited. Simple sufficient geometric conditions that imply the existence of the interpolant are derived in general. They require data points to be convex in a certain discrete sense. Since the geometric interpolation is based precisely on the known data only, one may consider it as the parametric counterpart to the polynomial function interpolation. The established result confirms the Höllig–Koch conjecture on the existence and the approximation order in the planar case for parametric polynomial curves of any degree stated quite a while ago.
ISSN:0021-9045
1096-0430
DOI:10.1016/j.jat.2022.105806