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Some splines produced by smooth interpolation

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  • Segeth, Karel

Abstract

The spline theory can be derived from two sources: the algebraic one (where splines are understood as piecewise smooth functions satisfying some continuity conditions) and the variational one (where splines are obtained via minimization of some quadratic functionals with constraints). We show that the general variational approach called smooth interpolation introduced by Talmi and Gilat covers not only the cubic spline but also the tension spline (called also spline in tension or spline with tension) in one or more dimensions. We show the results of a 1D numerical example that present the advantages and drawbacks of the tension spline.

Suggested Citation

  • Segeth, Karel, 2018. "Some splines produced by smooth interpolation," Applied Mathematics and Computation, Elsevier, vol. 319(C), pages 387-394.
    • Handle: RePEc:eee:apmaco:v:319:y:2018:i:c:p:387-394
    DOI: 10.1016/j.amc.2017.04.022
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    1. Segeth, Karel, 2015. "A periodic basis system of the smooth approximation space," Applied Mathematics and Computation, Elsevier, vol. 267(C), pages 436-444.
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