Stability results for approximation by positive definite functions on SO (3)
Journal of Approximation Theory
Numerical stability of nonequispaced fast Fourier transforms
Journal of Computational and Applied Mathematics
Probabilistic spherical Marcinkiewicz-Zygmund inequalities
Journal of Approximation Theory
Using NFFT 3---A Software Library for Various Nonequispaced Fast Fourier Transforms
ACM Transactions on Mathematical Software (TOMS)
Parameter estimation for exponential sums by approximate Prony method
Signal Processing
3D finite-difference synthetic acoustic log in cylindrical coordinates
Journal of Computational and Applied Mathematics
Nonequispaced Hyperbolic Cross Fast Fourier Transform
SIAM Journal on Numerical Analysis
Nonlinear Approximation by Sums of Exponentials and Translates
SIAM Journal on Scientific Computing
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A fast and reliable algorithm for the optimal interpolation of scattered data on the torus $\mathbb{T}^d$ by multivariate trigonometric polynomials is presented. The algorithm is based on a variant of the conjugate gradient method in combination with the fast Fourier transforms for nonequispaced nodes. The main result is that under mild assumptions the total complexity for solving the interpolation problem at $M$ arbitrary nodes is of order ${\cal O}(M\log M)$. This result is obtained by the use of localized trigonometric kernels where the localization is chosen in accordance with the spatial dimension $d$. Numerical examples show the efficiency of the new algorithm.