Specifications

University of Pretoria etd – Combrinck, M (2006)
The inversion method gives the smallest average error, followed by the cubic spline and
three point methods.
For unsmoothed data the equally spaced points slightly outperform the unequally spaced
points, but the reverse is true for smoothed data.
Smoothing of data seems to be the largest contributing factor to errors in noise-free data.
(a)
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Lagrange Three-Point
Cubic Spline
Inver se of In te grati o n
(b)
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(c)
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(d)
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135791113151719
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Percentage error
Figure 4-5: Comparison of differentiation methods applied to (a) unequally spaced points
without smoothing of data, (b) unequally spaced points with smoothing of data, (c) equally
spaced points without smoothing of data and (d) equally spaced points with smoothing.
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