BIT Numerical Mathematics

, Volume 14, Issue 2, pp 152–155 | Cite as

Some approximation properties of periodic parametric cubic splines

  • W. D. Hoskins
  • P. J. Ponzo


The parametric cubic splines interpolating to such closed curves as the circle and ellipse are derived in a form where their parameters are given by simple algebraic expressions.

The structure of these expressions enables the error in approximation of the given curves to be precisely determined and some additional features of the spline deduced.


Computational Mathematic Approximation Property Algebraic Expression Closed Curf Simple Algebraic Expression 
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    J. H. Ahlberg, E. N. Nilson, and J. L. Walsh,The Theory of Splines and Their Applications, Academic Press, 1967.Google Scholar
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    J. H. Ahlberg, E. N. Nilson, and J. L. Walsh,Polynomial Splines on the Real Line, Journal of Approximation Theory 3 (1970), 398–409.CrossRefGoogle Scholar
  3. 3.
    A. C. Aitken,Determinants and Matrices, Oliver and Boyd, 1958.Google Scholar
  4. 4.
    L. V. Atkinson and D. J. Evans,An Algorithm for the Solution of General Three-Term Systems, The Computer Journal, Vol. 13 (3) (1970).Google Scholar
  5. 5.
    M. Golomb,Approximation by Periodic Spline Interpolants on Uniform Meshes, Journal of Approximation Theory 1 (1968), 26–65.CrossRefGoogle Scholar

Copyright information

© BIT Foundations 1974

Authors and Affiliations

  • W. D. Hoskins
    • 1
    • 2
  • P. J. Ponzo
    • 1
    • 2
  1. 1.Computer Science DepartmentUniversity of ManitobaWinnipegCanada
  2. 2.Department of Applied MathematicsUniversity of WaterlooOntarioCanada

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