We investigate when a trigonometric polynomial p of degree M in d variables is uniquely determined by its sampled values p(xj) on a random set of points xj in the unit cube (the "sampling problem for trigonometric polynomials") and estimate the probability distribution of the condition number for the associated Vandermonde-type and Toeplitz-like matrices. The results provide a solid theoretical foundation for some efficient numerical algorithms that are already in use.
No takes yet. Share an insight, caveat, or question.
Bass et al. (2004) studied this question.
Synapse has enriched one closely related paper. Consider it for comparative context: