Reconstruction of functions

The usage of the inverse NFFT is e.g. shown in ./example/interpolation_1d, Figure 6, and ./example/glacier, Figure 7. For theoretical result see [16].

Figure: Real part of different interpolation polynomials for $N=20$ for the function $\sqrt {2}x_{+}^{1/2}$ sampled at $M=10$ nodes; $10$ iterations and the six kernels: Dirichlet, Fejer, Jackson ($m=2$), Jackson ($m=4$), Sobolev ($\alpha =1$), and inverse multi-quadric-type ( $c=1,\,\mu=2$).

Figure: Reconstruction of the glacier data set vol87.dat from [11] with radial ( $\hat w_{\mbox{\boldmath\scriptsize{${k}$}}}=\hat w_{\Vert\mbox{\boldmath\scriptsize{${k}$}}\Vert _2}$) inverse multi-quadric-type damping factors ( $c=1,\,\mu=1.4$); $M=8345$ nodes, $N=256$, $40$ iterations.