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The incorporation of boundary conditions in spline approximation problems

Part of the Lecture Notes in Mathematics book series (LNM,volume 630)

Abstract

The problem of determining polynomial spline approximations subject to derivative boundary conditions is considered. It is shown that if B-splines are employed as a basis, the incorporation of a variety of boundary conditions and the solution of the resulting equations for the B-spline coefficients can be carried out in an efficient and stable manner. The methods discussed can be applied to interpolating splines and to splines which approximate discrete data sets in the least squares sense. The boundary conditions can normally be incorporated by extending and refining existing algorithms rather than by designing entirely new ones.

Keywords

  • Spline Interpolation
  • Polynomial Spline
  • Stable Manner
  • Natural Spline
  • Small Relative Error

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1978 Springer-Verlag

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Cox, M.G. (1978). The incorporation of boundary conditions in spline approximation problems. In: Watson, G.A. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 630. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067696

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  • DOI: https://doi.org/10.1007/BFb0067696

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08538-6

  • Online ISBN: 978-3-540-35972-2

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