## Random sampling of multivariate trigonometric polynomials (2004)

by
Richard F. Bass
,
Karlheinz Gröchenig

Venue: | SIAM J. Math. Anal |

Citations: | 30 - 3 self |

### BibTeX

@ARTICLE{Bass04randomsampling,

author = {Richard F. Bass and Karlheinz Gröchenig},

title = {Random sampling of multivariate trigonometric polynomials},

journal = {SIAM J. Math. Anal},

year = {2004},

volume = {36},

pages = {795}

}

### Years of Citing Articles

### OpenURL

### Abstract

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.