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Stability results for scattered data interpolation by trigonometric polynomials. (English) Zbl 1146.65016
Interpolation on the multidimensional torus by multivariate trigonometric polynomials is considered. The data are not equidistant and a certain optimal interpolant is desired. This optimality is defined via the weighted sum of squares of its Fourier coefficients which is to be minimised. A stable algorithm to compute the solution of this problem using a variant of the conjugate gradient method is given, and its complexity is studied in detail. Several numerical examples are provided.

MSC:
65D05 Numerical interpolation
65F10 Iterative numerical methods for linear systems
65T40 Numerical methods for trigonometric approximation and interpolation
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65T50 Numerical methods for discrete and fast Fourier transforms
Software:
NFFT
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