Abstract
The aim of the present paper is to show that the convergence rate of the parametric cubic spline approximation of a plane curve is of order four instead of order three. For the first and second derivatives, the rates are of order three and two, respectively. Finally some numerical examples are given to illustrate the predicted error behaviour.
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References
J. H. Ahlberg, E. N. Nilson and J. L. Walsh,The Theory of Splines and their Applications, Academic Press, New York (1967).
M. S. Hanna, D. G. Evans and P. N. Schweitzer,On the approximation of plane curves by parametric cubic splines, BIT 26 (1986), 217–232.
W. D. Hoskins and P. J. Ponzo,Some approximation properties of periodic parametric cubic splines, BIT 14 (1974), 152–155.
H. Späth,Spline Algorithms for Curves and Surfaces, translated by W. D. Hoskins and H. W. Sager, Utilitas Publishing INC., Winnipeg (1974).
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Sakai, M., Usmani, R.A. On orders of approximation of plane curves by parametric cubic splines. BIT 30, 735–741 (1990). https://doi.org/10.1007/BF01933220
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DOI: https://doi.org/10.1007/BF01933220