Random sampling of multivariate trigonometric polynomials

被引：77

作者：

Bass, RF ^{[1
]}

Gröcheng, K

机构：

[1] Univ Connecticut, Dept Math, Storrs, CT 06269 USA

[2] GSF, Natl Res Ctr Environm & Hlth, Inst Biomath & Biometry, D-85764 Neuherberg, Germany

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2004年 / 36卷 / 03期

关键词：

sampling; band-limited functions; multivariate trigonometric polynomials; randomsampling; block Toeplitz matrix; Vandermonde matrix; condition number; metric entropy;

D O I：

10.1137/S0036141003432316

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：773 / 795

页数：23

共 39 条

[1] Beurling-Landau-type theorems for non-uniform sampling in shift invariant spline spaces [J].