Random Sampling of Multivariate Trigonometric Polynomials
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- 1 January 2005
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Mathematical Analysis
- Vol. 36 (3) , 773-795
- https://doi.org/10.1137/s0036141003432316
Abstract
We investigate when a trigonometric polynomial p of degree M in dvariables is uniquely determined by its sampled values p(x j ) on a random set ofpoints x j in the unit cube (the \sampling problem for trigonometric polynomials") and estimate the probability distribution of the condition number for theassociated Vandermonde-type and Toeplitz-like matrices. The results providea solid theoretical foundation for some ecient numerical algorithms that arealready in use.Keywords
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