Randomized approximation numbers on Besov classes with mixed smoothness

摘要

We study the Kolmogorov and the linear approximation numbers of the Besov classes MBp,theta Omega with mixed smoothness in the norm of L-q in the randomized setting. We first establish two discretization theorems. Then based on them, we determine the exact asymptotic orders of the Kolmogorov and the linear approximation numbers for certain values of the parameters p, q, theta. Our results show that the linear randomized methods lead to considerably better rates than those of the deterministic ones for 2 <= p <= q < infinity.