"Sampling numbers of smoothness classes via $\ell^1$-minimization"Jahn, ThomasWe study the recovery of multivariate functions f:Omega->C from m function values. The quantity of interest are sampling numbers, i.e., the minimal worst-case error that can be achieved by choosing the points at which f is evaluated and the recovery map that takes the vector of function values to an approximation for f. Using a recovery procedure based on l¹-minimization (basis pursuit denoising), we obtain asymptotic upper bounds for the sampling numbers that improve upon recently developed linear recovery methods. |
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