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Nonequispaced fast Fourier transform
Introduction
inversion

Inversion

The inverse nfft solves
$\displaystyle \sum_{\mbox{\boldmath\scriptsize {${k}$}}\in I_{\mbox{\boldmath\t...
              ...k}$}}\mbox{\boldmath\scriptsize {${x}$}}_j} \approx f_j \qquad (j=0,\hdots,M-1)$    
for arbitrary sampling sets $ {\cal X}:=\left\{\mbox{\boldmath {${x}$}}_j:\,j=0,\hdots,M-1\right\}\subset \mathbb{T}^d$


Related paper are

oKunis, S. and Potts, D.
Stability Results for Scattered Data Interpolation by Trigonometric Polynomials.
Preprint, Universität zu Lübeck,   (full paper ps, pdf)   2005

oBöttcher, A. and Potts, D.
Probability against condition number and sampling of multivariate trigonometric random polynomials.
Electron. Trans. Numer. Anal. , accepted,   (full paper ps, pdf),   2006

oBöttcher, A., Potts, D. and Wenzel, D
A probability argument in favor of ignoring small singular values.
Operator Theory: Advances and Applications, accepted,   (full paper ps, pdf),   2006