Specifications

University of Pretoria etd – Combrinck, M (2006)
enhanced in derivative calculations), computer round-off effects and how accurately the
causative function can be approximated locally by a second order polynomial.
4.4.2.2.2 Derivative of cubic spline interpolated function (referred to as “cubic spline derivative
method”)
The Lagrange three-point method will give analytically correct results for functions of
order one or two. The most intuitive way to extend the approximation for a wider range
of functions is to increase the degree of the Lagrange approximating polynomial.
However, this does not always improve the final result as is illustrated by Burden and
Faires (1993) in Figure 4-4.
Figure 4-4 A Lagrange interpolating polynomial fitted to the data points outlining the back of a
duck (top) and a cubic spline curve fitted to the same data points (bottom). (From Burden and
Faires, 1993, Figures 3.11 and 3.12)
Lagrange interpolation requires that the approximated function values on the measured
positions be exactly equal to the discrete data points. This introduces unwanted
oscillations which are especially detrimental to any consecutive derivative calculations. An
alternative is to fit higher order functions using the least squares errors approach.
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