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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

oB÷ttcher, 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

oB÷ttcher, 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