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An Introduction to Non-Linear Splines

  • Helmut Werner
Part of the NATO Advanced Study Institutes Series book series (ASIC, volume 49)

Abstract

We introduce functions termed non-linear splines because they belong to a class of k-times differentiable funtions (k N) and their restrictions to certain subintervals (defined by knots) are non-linearly dependent on the parameters in contrast to the splines usually considered. It is shown that use of these non-linear splines in interpolation, approximation and numerical quadrature or ordinary differential equations is widely parallel to the linear case as far as numerical work and stability is concerned, while it allows us to take into account special properties of the functions which the spline is used to replace.

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Copyright information

© Springer Science+Business Media Dordrecht 1979

Authors and Affiliations

  • Helmut Werner
    • 1
  1. 1.Institut für Numerische und Instrumenteile Mathematik und Rechenzentrumder Westfälischen Wilhelms UniversitätMünster/WestfalenGermany

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