Figures and compare the test interpolation errors and discrete responses of methods based on the B-spline function and the lower smoothness function . The latter method has a slight but visible performance advantage and a slightly wider discrete spectrum.
Figure 23 Interpolation error of the third-order B-spline interpolant (dashed line) compared to that of the lower smoothness spline interpolant (solid line).
Figure 24 Discrete interpolation responses of third-order B-spline and lower smoothness spline interpolants (left) and their discrete spectra (right) for x=0.7.
Blu et al. (1998) have developed a general approach for constructing non-smooth piece-wise functions with optimal interpolation properties. However, the gain in accuracy is often negligible in practice. In the rest of this paper, I use the classic B-spline method.