BIT Numerical Mathematics

, Volume 30, Issue 4, pp 735–741 | Cite as

On orders of approximation of plane curves by parametric cubic splines

  • Manabu Sakai
  • Riaz A. Usmani
Part II Numerical Mathematics


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.

AMS Subject Classification

Primary 41A15 Secondary 41A25, 65D05 


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  1. 1.
    J. H. Ahlberg, E. N. Nilson and J. L. Walsh,The Theory of Splines and their Applications, Academic Press, New York (1967).Google Scholar
  2. 2.
    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.Google Scholar
  3. 3.
    W. D. Hoskins and P. J. Ponzo,Some approximation properties of periodic parametric cubic splines, BIT 14 (1974), 152–155.Google Scholar
  4. 4.
    H. Späth,Spline Algorithms for Curves and Surfaces, translated by W. D. Hoskins and H. W. Sager, Utilitas Publishing INC., Winnipeg (1974).Google Scholar

Copyright information

© BIT Foundations 1990

Authors and Affiliations

  • Manabu Sakai
    • 1
    • 2
  • Riaz A. Usmani
    • 1
    • 2
  1. 1.Department of Mathematics, Faculty of ScienceUniversity of KagoshimaKagoshimaJapan
  2. 2.Department of Applied MathematicsUniversity of ManitobaWinnipegCanada

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